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General decay for a nonlinear pseudo-parabolic equation with viscoelastic term

100%

Vu N. T. , Dung D. B. , Dung H. T. H.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

737--751

This work is concerned with a multi-dimensional viscoelastic pseudo-parabolic equation with critical Sobolev exponent. First, with some suitable conditions, we prove that the weak solution exists globally. Next, we show that the stability of the system holds for a much larger class of kernels than the ones considered in previous literature. More precisely, we consider the kernel g:[0,∞)⟶(0,∞) satisfying g′(t)⩽−ξ(t)G(g(t)) , where ξ and G are functions satisfying some specific properties.

On some nonlinear hyperbolic p(x,t)-Laplacian equations

100%

Ahmedatt T. , Touzani A. , Aberqi A. , Yazough C.

Journal of Applied Analysis

2018

tom Vol. 24, nr 1

55--69

This paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equation Utt=Lu+f(x,t) in ΩT=Ω×(0,T), where L is a nonlinear operator and ϕ(x,t,⋅), f(x,t) and the exponents of the nonlinearities p(x,t) and μ(x,t) are given functions.

Existence and uniqueness of the weak solution for Keller-Segel model coupled with Boussinesq equations

80%

Slimani A. , Bouzettouta L. , Guesmia A.

tom Vol. 54, nr 1

558--575

Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method.

Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

80%

Bidi Y. , Beniani A. , Zennir K. , Himadan A.

tom Vol. 54, nr 1

245--258

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.