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In this paper, we study a one‐dimension nonlinear problem for thermoelastic coupled beam equations with memory term. Using the Faedo–Galerkin method and the linearization method for nonlinear terms, we first prove the local existence and the uniqueness of a weak solution. Next, by establishing assumptions and constructing energy functionals suitably, we consider the global existence and general decay behavior of the solution. Finally, the blow‐up property in the special case of this problem is also given. [ABSTRACT FROM AUTHOR]

In this paper, numerical results for a fourth‐order nonlinear wave equation of Kirchhoff type with a viscoelastic term are established. First, the existence and uniqueness of a solution is proved by applying the Faedo–Galerkin method and the weak compact method. Next, an algorithm to the initial boundary value problem for a nonlinear evolution equation of fourth order is studied where the spatial‐variable discretization and time‐variable discretization are constructed to approximate derivatives by the difference schemes. Finally, the numerical results are shown to present the errors of proposed algorithm. Simulations of the approximate solution and the exact solution are also visualized. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a nonlinear pseudoparabolic equation in an annular with Robin–Dirichlet conditions. At first, by applying the standard Faedo–Galerkin method, we prove existence and uniqueness results. Next, using concavity method, we prove blow‐up results for solutions when the initial energy is nonnegative or negative, then we also establish the lifespan for the equation via finding the upper bound and the lower bound for the blow‐up times. Finally, we give a sufficient condition for the global existence and decay of weak solutions. [ABSTRACT FROM AUTHOR]

This note presents corrections to our paper. We also give remarks and additions related to other papers. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the set of solutions of a nonlinear functional integral equation in N variables in a Fréchet space. Applying a fixed point theorem of Krasnosel'skii type and a structure theorem of Krasnosel'skii and Perov, a sufficient condition is established such that the set of solutions is a continuum, that is, nonempty, compact and connected. Furthermore, based on Aronszajn type results and a theorem proved by Vidossich, we show that this solutions set is also a compact [ABSTRACT FROM AUTHOR]

The paper is devoted to the study of a system of semilinear wave equations associated with the helical flows of Maxwell fluid. First, based on Faedo-Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions via the construction of a suitable Lyapunov functional. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Motivated by recent known results about the solvability of nonlinear functional integral equations in one, two or N variables, this paper proves the existence of asymptotically stable solutions for a mixed functional integral equation in N variables with values in a general Banach space via a fixed point theorem of Krasnosels'kiĭ type. In order to illustrate the results obtained here, an example is given. [ABSTRACT FROM AUTHOR]

The HIV epidemic in Vietnam is fueled by injecting drug use. Since HIV emerged, because of a law-enforcement-focused drug policy and response, injecting drug users (IDUs) frequently experience drug detention and compulsory treatment. It has taken more than a decade to shift the focus from punitive to liberal policies. This overview presents a brief discussion on policies, responses, and experiences to identify implications. Related literature including government policies, peer-reviewed articles, and reports has been reviewed. The HIV epidemic in IDUs accelerated rapidly in an environment characterized by a lack in understanding and recognition of significance. There was limited leadership and weak direction to implement a countrywide response. Policies and responses gradually shifted to a harm reduction approach and recognized the need for harmonization, relating common features of drug and HIV. The review identifies that government leadership is crucial for supportive policies and long-term strategies. A multi-sectoral collaboration and continuous resource allocation with national priorities is essential to impact on the epidemic. In this review the context of these issues in policies and responses are highlighted and discussed, which gradually can lead towards the development of a substantial response for the drug use-driven HIV epidemic in Vietnam. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a system of nonlinear equations with nonlinear boundary conditions. First, on the basis of the Faedo-Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, the exponential decay property of the global solution via the construction of a suitable Lyapunov functional is presented. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]