Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

Niu, Weisheng; Meng, Qing Rui; Chai, Xiaojuan

doi:10.1080/00036811.2020.1721470

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“…In [10], El Hachimi, Igbida and Jamea explained the existence of entropy solution of a nonlinear parabolic problem by using a time discretization of continuous problem. Besides that, the existence and uniqueness of degenerate parabolic equations of type (1.1) was proved by Weisheng et al in [24].…”

Section: Introductionmentioning

confidence: 94%

Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method

Hmidouch,

Jamea,

Laghdir

2023

Mathematical Modelling and Analysis

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Section: Introductionmentioning

confidence: 94%

Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method

Hmidouch,

Jamea,

Laghdir

2023

Mathematical Modelling and Analysis

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show abstract

Dynamical behavior of a degenerate parabolic equation with memory on the whole space

Guo,

Leng

2024

Bound Value Probl

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This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on $\mathbb{R}^{n}$ R n . Since the corresponding equation includes the degenerate term $\operatorname{div}\{a(x)\nabla u\}$ div { a ( x ) ∇ u } , it requires us to give appropriate assumptions about the weight function $a(x)$ a ( x ) for studying our problem. Based on this, we first obtain the existence of a bounded absorbing set, then verify the asymptotic compactness of a solution semigroup via the asymptotic contractive semigroup method. Finally, the existence and uniqueness of global attractors are proved. In particular, the nonlinearity f satisfies the polynomial growth of arbitrary order $p-1$ p − 1 ($p\geq 2$ p ≥ 2 ) and the idea of uniform tail-estimates of solutions is employed to show the strong convergence of solutions.

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Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

Cited by 2 publications

References 30 publications

Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method

Existence of Entropy Solution for a Nonlinear Parabolic Problem in Weighted Sobolev Space via Optimization Method

Dynamical behavior of a degenerate parabolic equation with memory on the whole space

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