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Inhibitor tolerance is still a bottleneck for lactic acid bacteria in lignocellulose biorefinery, while it is hard to obtain one engineered strain with strong tolerance to all inhibitors. Herein, a robust adapted d-lactic acid producing strain Pediococcus acidilactici XH11 was obtained by 111 days' long-term adaptive evolution in undetoxified corncob prehydrolysates. The adapted strain had higher inhibitors tolerance compared to the parental strain, primarily due to its increased conversion capacities of four typical aldehyde inhibitors (furfural, HMF, vanillin, and 4-hydroxybenzaldehyde). One-pot simultaneous saccharification and co-fermentation was successfully achieved using the whole slurry of acid-pretreated corncob without solid-liquid separation and detoxification, by applying the adapted P. acidilactici XH11. Finally, 61.9 g/L of d-lactic acid was generated after 96 h' fermentation (xylose conversion of 89.9 %) with the overall yield of 0.48 g/g dry corncob. This study gave an important option for screening of industrial strains in cellulosic lactic acid production processes.

In this paper, we present a rigorous mathematical analysis of a free boundary problem modeling the growth of a vascular solid tumor with a necrotic core. If the vascular system supplies the nutrient concentration $\sigma$ to the tumor at a rate $\beta$, then $\frac{\partial\sigma}{\partial\bf n}+\beta(\sigma-\bar\sigma)=0$ holds on the tumor boundary, where $\bf n$ is the unit outward normal to the boundary and $\bar\sigma$ is the nutrient concentration outside the tumor. The living cells in the nonnecrotic region proliferate at a rate $\mu$. We show that for any given $\rho>0$, there exists a unique $R\in(\rho,\infty)$ such that the corresponding radially symmetric solution solves the steady-state necrotic tumor system with necrotic core boundary $r=\rho$ and outer boundary $r=R$; moreover, there exist a positive integer $n^{**}$ and a sequence of $\mu_n$, symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solution for each $\mu_n$ (even $n\ge n^{**})$., Comment: 29 pages

This paper concerns a free boundary problem modeling tumor growth with angiogenesis and two time delays. The two delays represent the time taken for cells to undergo mitosis and modify the rate of cell loss because of apoptosis, respectively. We study the stability of stationary solutions and find that Hopf bifurcation occurs under some conditions, which extends the results of Xu. Furthermore, numerical simulations are performed to investigate the relationship among the rate of angiogenesis, two time delays and Hopf bifurcation., 14 pages, 6 figures

We consider a free boundary tumor model under the presence of angiogenesis and time delays in the process of proliferation, in which the cell location is incorporated. It is assumed that the tumor attracts blood vessels at a rate proportional to \begin{document}$ \alpha $\end{document}, and a parameter \begin{document}$ \mu $\end{document} is proportional to the 'aggressiveness' of the tumor. In this paper, we first prove that there exists a unique radially symmetric stationary solution \begin{document}$ \left(\sigma_{*}, p_{*}, R_{*}\right) $\end{document} for all positive \begin{document}$ \alpha $\end{document}, \begin{document}$ \mu $\end{document}. Then a threshold value \begin{document}$ \mu_\ast $\end{document} is found such that the radially symmetric stationary solution is linearly stable if \begin{document}$ \mu and linearly unstable if \begin{document}$ \mu>\mu_\ast $\end{document}. Our results indicate that the increase of the angiogenesis parameter \begin{document}$ \alpha $\end{document} would result in the reduction of the threshold value \begin{document}$ \mu_\ast $\end{document}, adding the time delay would not alter the threshold value \begin{document}$ \mu_\ast $\end{document}, but would result in a larger stationary tumor, and the larger the tumor aggressiveness parameter \begin{document}$ \mu $\end{document} is, the greater impact of time delay would have on the size of the stationary tumor.

This paper is concerned with a nonlinear free boundary problem modeling the growth of spherically symmetric tumors with angiogenesis, set with a Robin boundary condition, in which, both nonnecrotic tumors and necrotic tumors are taken into consideration. The well-posedness and asymptotic behavior of solutions are studied. It is shown that there exist two thresholds, denoted by σ and σ ∗ , on the surrounding nutrient concentration σ . If σ ≤ σ , then the considered problem admits no stationary solution and all evolutionary tumors will finally vanish, while if σ > σ , then it admits a unique stationary solution and all evolutionary tumors will converge to this dormant tumor; moreover, the dormant tumor is nonnecrotic if σ σ ≤ σ ∗ and necrotic if σ > σ ∗ . The connection and mutual transition between the nonnecrotic and necrotic phases are also given.

In view of the current problems in China’s logistics industry, such as easy delay of goods distribution information, inconvenient location of express delivery stations for customers, and information level to be improved, the “internet plus Logistics” method is used to improve the efficiency of resource allocation. It can not only effectively play the positive effect of the logistics network, but also achieve the goal of orderly and efficient logistics distribution at lower logistics costs. Therefore, it is very important to discuss the social and economic significance of a logistics management distribution system based on logistics network. Through the organic connection between the central processing unit and each functional module, the system can not only enable customers to obtain corresponding logistics information in real time, but also realize distribution for other customers in the same area under convenient conditions. As a result, the system can not only reduce the number of delivery personnel at logistics terminals, reduce the operating costs of logistics companies and improve the efficiency of logistics distribution in the region, but also provide part-time jobs for the delivery personnel, thus realizing the purpose of rewarding the delivery personnel according to the actual number and weight of the delivery items, increasing personal income and driving the development of the regional economy.

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system - div ( h 1 ( x ) | ∇ u | p - 2 ∇ u ) = d ( x ) | u | r - 2 u + G u ( x , u , υ ) - div ( h 2 ( x ) | ∇ υ | q - 2 ∇ υ ) = f ( x ) | υ | s - 2 υ + G υ ( x , u , υ ) u = υ = 0 in Ω in Ω on ∂ Ω where Ω is a bounded domain in R N with smooth boundary ∂Ω, N≥2, 1 < r < p < ∞, 1 < s < q < ∞; h1(x) and h2(x) are allowed to have “essential” zeroes at some points in Ω ; d ( x ) | u | r - 2 u and f ( x ) | υ | s - 2 υ are small sources with Gu(x,u,v), Gv(x,u,v) being their high-order perturbations with respect to (u,v) near the origin, respectively.

We consider a free boundary problem modeling the growth of angiogenesis tumor with inhibitor, in which the tumor aggressiveness is modeled by a parameter \begin{document}$μ$\end{document} . The existences of radially symmetric stationary solution and symmetry-breaking stationary solution are established. In addition, it is proved that there exist a positive integer \begin{document}$m^{**}$\end{document} and a sequence of \begin{document}$μ_m$\end{document} , such that for each \begin{document}$μ_m(m > m^{**})$\end{document} , the symmetry-breaking stationary solution is a bifurcation branch of the radially symmetric stationary solution.

In order to explore the influence of different stepwise heating methods for the acid-producing phase on the gas production of the methane-producing phase, the stepwise heating method with the best acidification, the highest gas production and the best energy-saving effect was obtained. Using cow dung as the raw material, the acid-producing phase is used for stepwise warming, the temperature increase range is 20–35 °C, set three different step-by-step heating methods respectively: the first group is heated by 5 °C/2 d, and the second group is heated by 2.5 °C/d; the third group was heated by 2 °C, 8 °C and 5 °C respectively once every other day; constant temperature fermentation after heating to 35 °C; and a set of acid-producing phase constant temperature 35 °C fermentation; the methane-producing phase is always fermented at a constant temperature of 38 °C; analyze the changes of different parameters. The results show that, in the first group, the total mass concentration of volatile fatty acids is 9372.46 mg/L; the proportion of the total concentration of acetic acid butyric acid to the mass concentration of volatile fatty acids is 77 %; the cumulative gas production volume is 6253 mL, and the cumulative methane production volume is 3741 mL, the total energy consumption is 638.32 kJ, and the heat generated by biogas combustion is 156.33 kJ; the difference between system energy consumption and production capacity is 481.99 kJ. As for the second group, the total mass concentration of volatile fatty acids is 7810.49 mg/L, and the proportion of the total concentration of acetic acid butyric acid to the mass concentration of volatile fatty acids is 74 %. The cumulative gas production volume is 4583 mL, and the cumulative methane production volume is 2521 mL. The total energy consumption is 629.46 kJ, and the heat generated by biogas combustion is 114.58 kJ. Moreover, the difference between system energy consumption and production capacity is 514.88 kJ. In the third group, the total mass concentration of volatile fatty acids is 7664.71 mg/L, the proportion of the total concentration of acetic acid butyric acid to the mass concentration of volatile fatty acids is 75 %; the cumulative gas production volume is 4606 mL, the cumulative methane production volume is 2579 mL. The total energy consumption is 624.18 kJ, and the heat generated by biogas combustion is 115.15 kJ. The difference between system energy consumption and production capacity is 509.03 kJ. In the constant temperature 35 °C group, by contrast, the cumulative gas production volume is 6565 mL, the cumulative methane production volume is 3939 mL. The total energy consumption is 765.74 kJ, and the heat generated by biogas combustion is 164.13 kJ. The difference between system energy consumption and production capacity is 601.61 kJ. According to the comparative analysis of the three groups, the first group has the best acidification effect and highest gas production, and the difference in energy consumption compared with the constant temperature group is also lower, which is more economical. Therefore, the step-by-step heating method of 5 °C/2 d is the best.

This paper is concerned with the time delayed Nicholson’s blowflies equation with degenerate diffusion. We prove the existence and uniqueness of the positive steady state solution under the Dirichlet boundary condition and we show the stability of the nontrivial steady state.

This paper is concerned with the bifurcation phenomenon of a free-boundary problem modeling the tumor growth under the action of angiogenesis and inhibitor. Taking the surface tension coefficient γ as a bifurcation parameter, we prove that there exist a positive integer $m^{**}$ and a sequence of $\gamma_{m}$ such that, for every $\gamma_{m}$ ( $m>m^{**}$ ), symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solutions.

This paper is concerned with a class of nonlinear diffusion equations coupled by the nonlinear boundary sources on the exterior domain of the unit ball in \(\mathbb R^N\). We are interested in the critical curves which can describe the large time behavior of the solutions. It is shown that the critical global existence curve coincides with the critical Fujita curve for the system we considered.

In this paper, polypropylene (PP) as main material, magnesium hydroxide as flame retardant, effects of flame retardant synergist cobalt zeolite on flame retardant PP composite flame retardant properties, mechanical properties and thermal degradation behavior. The results show that, the reaction time is 3h, the reaction temperature is 400 ℃ , the loading is 7%,the flame-retardant properties of PP composites were improved obviously, the horizontal burning rate is 20.6mm/min, the limiting oxygen index reached 22.6%; little effect on the mechanical properties, tensile strength is up to 22.1MPa, the impact strength is 4.25KJ/m2; introducing cobalt zeolite change the thermal degradation process of magnesium hydroxide / PP system, decrease the thermal decomposition rate of PP composite, improve the thermal stability of the composites at high temperature.

This paper deals with a free boundary problem modeling tumor growth with inhibitors. This problem has a unique radially symmetric stationary solution with radius r = R s . The tumor aggressiveness is modeled by a positive tumor aggressiveness parameter μ . It is shown that there exist a positive integer m ∗ ∗ ∈ R and a sequence of μ m , such that for each μ m ( m > m ∗ ∗ ) , symmetry-breaking solutions bifurcate from the radially symmetric stationary solutions.

This paper deals with a parabolic system coupled via nonlocal sources, subjecting to positive Dirichlet boundary value conditions. By using the super-, sub-solution methods and techniques, and piecewise functions, the blow-up criteria and global boundedness of nonnegative solutions are determined. The results show the positive boundary value e 0 plays an important role in the case of blow-up.

This paper investigates the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, and weight function, and complemented by homogeneous Dirichlet boundary conditions. The criteria are proposed to identify simultaneous and non-simultaneous blow-up solutions. Moreover, the related classification for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang [12].

In this paper we consider the weighted p-Laplacian \(-\mathrm{div}(|x|^\alpha |\nabla u|^{p-2}\nabla u)+ |x|^\gamma |u|^{q-1}u=0\) in \(B{\setminus }\{0\}\), where \(B\subset \mathbb {R}^N(N\ge 2)\) is the unit ball centered at the origin, \(\alpha \ge p-N\), \(\gamma >-N\) and \(q>p-1>0\). Classification of singularities for all positive solutions will be presented via two thresholds on \(\alpha \).

This paper deals with the large-time behaviour of solutions to the fast diffusive Newtonian filtration equations coupled via the nonlinear boundary sources. A result of Fujita type is obtained by constructing various kinds of upper and lower solutions. In particular, it is shown that the critical global existence curve and the critical Fujita curve concide for the multi-dimensional system. This is quite different from the known results obtained in Wang, Zhou and Lou [‘Critical exponents for porous medium systems coupled via nonlinear boundary flux’, Nonlinear Anal.7(1) (2009), 2134–2140] for the corresponding one-dimensional problem.

This paper considers the finite time blow-up of nonnegative solutions for a nonlinear diffusion system with a more complicated source term, which is a product of localized source, local source, weight function, and complemented by homogeneous Dirichlet boundary conditions. It is proved that there exists initial data such that simultaneous or non-simultaneous blow-up occur. Moreover, the related classifications for the four parameters in the model is optimal and complete. The results extend those in Zhang and Yang (J. Appl. Math. Comput. 32:429–441, 2010).

This paper deals with a degenerate parabolic system with nonlocal sources. It is prove that if pc = p1q1 − (m − p2)(n − q2) 0, there are solutions that blow-up and others that are global. When pc = 0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.

In this paper, we establish the blow-up theorems of Fujita type for a class of homogeneous Neumann exterior problems of quasilinear convection–diffusion equations. The critical Fujita exponents are determined and it is shown that the exponents belong to the blow-up case under any nontrivial initial data. Copyright © 2010 John Wiley & Sons, Ltd.

This paper deals with the large-time behaviour of solutions to the exterior problem of the non-Newtonian filtration equation with first-order term and nonlinear boundary source. In particular, the critical global exponent and the critical Fujita exponent are determined or estimated. An interesting phenomenon is shown: there exists a threshold value for the coefficient of the first-order term such that the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this value.

This paper is concerned with the porous medium equations for coupling via nonlinear boundary flux; we obtain the critical global existence curve and the critical Fujita curve for the problem, considered by constructing the self-similar supersolutions and subsolutions.

In this paper we consider a singular diffusion equation arising in phase transition and investigate its self-similar entropy solutions with jump hypersurfaces. The existence, nonexistence and uniqueness theorems of such solutions are established. We also discuss some properties of this kind of solutions including monotonicity and asymptotic behavior.

This paper is concerned with the large time behavior of solutions to two types of nonlinear diffusion equations with nonlinear boundary sources on the exterior domain of the unit ball. We are interested in the critical global exponent q 0 and the critical Fujita exponent q c for the problems considered, and show that q 0 = q c for the multi-dimensional porous medium equation and non-Newtonian filtration equation with nonlinear boundary sources. This is quite different from the known results that q 0 q c for the one-dimensional case.

This paper is concerned with large time behavior of solutions to the homogeneous Neumann problem of the non-Newtonian filtration equation. It is shown that the critical Fujita exponent for the problem considered is determined not only by the spatial dimension and the nonlinearity exponent, but also by the coefficient k of the first-order term. In fact, we show that there exist two thresholds k∞ and k1 on the coefficient k of the first-order term, and the critical Fujita exponent is a finite number when k is between k∞ and k1, while the critical exponent does not exist when k⩽k∞ or k⩾k1. Copyright © 2007 John Wiley & Sons, Ltd.

The paper concerns the existence theorem of weak solutions for the initial-boundary value problem of a nonlinear diffusion equation with convection. The equation may be regarded as a generalized non-Newtonian polytropic filtration equation. By doing the necessary BV estimate and other estimates for approximating solutions, we establish the existence theorem.

This paper deals with the exterior problem of the Newtonian filtration equation with nonlinear boundary sources. The large time behavior of solutions including the critical Fujita exponent are determined or estimated. An interesting phenomenon is illustrated that there exists a threshold value for the coefficient of the lower order term, which depends on the spacial dimension. Exactly speaking, the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this threshold.

In this paper, we establish the blow-up theorems of the Fujita type for a class of homogeneous Neumann problems of quasilinear equations with convection terms. The critical Fujita exponents are determined and it is shown that the exponents belong to the blow-up case under any nontrivial initial data. An interesting phenomenon is exploited such that the critical Fujita exponent even could be infinite for the model considered in the paper owing to the effect of convection.

This paper is concerned with the p-Laplacian equation with singular sources which is allowed to change sign in a ball. The singularity may occur at the zero points of solutions and on the boundary. Using the upper and lower solutions method, we establish the existence of positive radial solutions for the problem considered. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper, we consider the initial-boundary value problem of a nonlinear parabolic equation with double degeneracy, and establish the existence and uniqueness theorems of renormalized solutions which are stronger than $BV$ solutions.