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We are concerned with extinction properties for a p-Laplacian equation with gradient source and absorption terms under nonlinear boundary condition. Based on the integral norm estimate method and the technique of differential inequalities, we establish some extinction results and the precise decay estimates of extinction solutions for this problem. Furthermore, we believe that the arguments used in this paper can also be applicable to the problem with nonlocal source instead of a gradient source. [ABSTRACT FROM AUTHOR]

In this paper, we discuss global existence, boundness, blow-up and extinction properties of solutions for the Dirichlet boundary value problem of the $ p $-Laplacian equations with logarithmic nonlinearity $ u_{t}-{\rm{div}}(|\nabla u|^{p-2}\nabla u)+\beta|u|^{q-2}u = \lambda |u|^{r-2}u\ln{|u|} $, where $ 1 < p < 2 $, $ 1 < q\leq2 $, $ r > 1 $, $ \beta, \lambda > 0 $. Under some appropriate conditions, we obtain the global existence of solutions by means of the Galerkin approximations, then we prove that weak solution is globally bounded and blows up at positive infinity by virtue of potential well theory and the Nehari manifold. Moreover, we obtain the decay estimate and the extinction of solutions.

In this paper, we study the initial boundary value problem for a class of fractional p-Laplacian Kirchhoff type diffusion equations with logarithmic nonlinearity. Under suitable assumptions, we obtain the extinction property and accurate decay estimates of solutions by virtue of the logarithmic Sobolev inequality. Moreover, we discuss the blow-up property and global boundedness of solutions.

This paper mainly deals with extinction and non-extinction of weak solutions for a non-Newton polytropic filtration system coupled with non-local source terms under homogeneous Dirichlet boundary condition by comparing the exponents of nonlinear terms. Particularly, precise decay estimates of extinction solutions in the whole dimensional space are also established. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the extinction and non-extinction properties of solutions for the following fractional p -Kirchhoff problem { u t + M ([ u ] s , p p) (− Δ) p s u = λ | u | r − 2 u − μ | u | q − 2 u (x , t) ∈ Ω × (0 , ∞) , u = 0 (x , t) ∈ (R N ∖ Ω) × (0 , ∞) , u (x , 0) = u 0 (x) x ∈ Ω , where [ u ] s , p is the Gagliardo seminorm of u , Ω ⊂ R N is a bounded domain with Lipschitz boundary, (− Δ) p s is the fractional p -Laplacian with 0 < s < 1 < p < 2 , M : [ 0 , ∞) → (0 , ∞) is a continuous function, 1 < q ≤ 2 , r > 1 and λ , μ > 0. Under suitable assumptions, we obtain the extinction of solutions. To get more precisely decay estimates of solutions, we develop the Gagliardo-Nirenberg inequality. Moreover, the non-extinction property of solutions is also investigated. [ABSTRACT FROM AUTHOR]

We investigate the extinction properties of non-negative nontrivial weak solutions of the initial-boundary value problem for a p-Laplacian evolution equation with nonlinear gradient source and absorption terms. [ABSTRACT FROM AUTHOR]

This paper deals with the extinction properties of solutions for the homogeneous Dirichlet boundary value problem with the nonlocal source and interior absorption [ABSTRACT FROM AUTHOR]

Abstract: We investigate the extinction, non-extinction and decay estimates of non-negative nontrivial weak solutions of the initial-boundary value problem for the -Laplacian equation with nonlocal nonlinear source and interior linear absorption. We show that the critical exponent of extinction for the weak solution is determined by the competition of two nonlinear terms, and decay estimates depend on the choices of initial data, coefficients and domain. [Copyright &y& Elsevier]

Abstract: We consider the extinction properties of solutions for the homogeneous Dirichlet boundary value problem for the -Laplacian equation with and . For , it is known that is the critical extinction exponent for the weak solution. For , we show that is still the critical extinction exponent when . Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived. However, extinction can always occur when . [Copyright &y& Elsevier]