Attractors for a class of doubly nonlinear parabolic systems

Ouardi, Hamid El; Hachimi, Abderrahmane El

doi:10.14232/ejqtde.2006.1.1

Cited by 11 publications

(7 citation statements)

References 10 publications

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“… showed the exponential growth and blow‐up of solutions with negative or positive initial energy by constructing differential inequality. We also refer to for related results.…”

Section: Introductionmentioning

confidence: 99%

Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

Zhang

Liu

2019

Mathematische Nachrichten

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In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms.We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively. K E Y W O R D S blow-up, decay, generalized Boussinesq equation, global existence, nonlinear boundary condition M S C ( 2 0 1 0 ) 35K05, 35K61, 35K70

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“… showed the exponential growth and blow‐up of solutions with negative or positive initial energy by constructing differential inequality. We also refer to for related results.…”

Section: Introductionmentioning

confidence: 99%

Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

Zhang

Liu

2019

Mathematische Nachrichten

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“…In the non-Newtonian fluids theory, (p 1 , p 2 ) is a characteristic quantity of the fluids, there have been many results about the existence, uniqueness of the solutions. We refer the readers to the bibliography given in [7,9,10,11,28,31] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Study of solutions to a class of certain parabolic systems with variable exponents

Ouardi¹,

Ghabbar

2017

Int. J. Simul. Multisci. Des. Optim.

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“…When = 0, the class of equation (1.1) can also be as a special case of doubly nonlinear parabolic-type equations (or the porous medium equation) [5,13] It should be noted that questions of solvability, local and global in time, asymptotic behavior and blow-up of initial boundary value problems and initial value problems for equation of the type (1.7) were investigated by many authors. We only mention the work [13,14] for this class equation.…”

Section: Introductionmentioning

confidence: 99%

Exponential Growth of Solution for a Class of Reaction Diffusion Equation with Memory and Multiple Nonlinearities

Dang¹,

Hu²,

Xia³

et al. 2017

Research in Applied Mathematics

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Attractors for a class of doubly nonlinear parabolic systems

Cited by 11 publications

References 10 publications

Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

Global existence, asymptotic stability and blow‐up of solutions for the generalized Boussinesq equation with nonlinear boundary condition

Study of solutions to a class of certain parabolic systems with variable exponents

Exponential Growth of Solution for a Class of Reaction Diffusion Equation with Memory and Multiple Nonlinearities

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