Global attractors for nonlinear parabolic equations with nonstandard growth and irregular data

Niu, Weisheng; Chai, Xiaojuan

doi:10.1016/j.jmaa.2017.01.049

Cited by 6 publications

(8 citation statements)

References 40 publications

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“…Now, we deal with the second and the third terms on the left-hand side of Equation (19) in turn by Lemma 4, it is easy to obtain…”

Section: The Existence Resultsmentioning

confidence: 99%

“…In recent years, a large number of literatures have studied the existence and upper semicontinuity of attractors for evolution equations satisfying nonstandard growth conditions (see, e.g., [13,14,19,20,[22][23][24]). In [13,14,[22][23][24], under the different conditions, the continuity (w.r.t.…”

Section: Introductionmentioning

confidence: 99%

“…initial conditions and parameter) of solutions, the existence and upper semicontinuity of global attractors, and pullback attractors were obtained, respectively, but the growth exponents depend only on spatial variables. In [19,20], the authors studied the following nonlinear parabolic equation:…”

Section: Introductionmentioning

confidence: 99%

“…initial conditions and parameter) of solutions, the existence and upper semicontinuity of global attractors, and pullback attractors were obtained, respectively, but the growth exponents depend only on spatial variables. In [19, 20], the authors studied the following nonlinear parabolic equation:

\begin{align} u_t - \text{div} {\left\lbrace |\nabla u|^{p(x)-2} \nabla u\right\rbrace} + f(x,u)=g. \end{align}

First, the existence and fractal dimension of global attractors were obtained.…”

Section: Introductionmentioning

confidence: 99%

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Upper semicontinuity of pullback D$\mathcal {D}$‐attractors for nonlinear parabolic equation with nonstandard growth condition

Liu

Huang

2023

Mathematische Nachrichten

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This paper is devoted to the well‐posed problem and the existence of pullback ‐attractors for a class of nonlinear parabolic equation with nonstandard growth condition. First, by making use of Galerkin's method and monotone operator method, the existence of solutions is proved in Orlicz–Sobolev space with variable exponents depending on time and space, then the uniqueness and continuity of solutions are also obtained. Finally, by verifying the pullback ‐asymptotic compactness, the existence of pullback ‐attractors is proved. In particular, the upper semicontinuity of pullback ‐attractors of the corresponding equation with respect to the disturbance parameter λ is also proved.

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“…Now, we deal with the second and the third terms on the left-hand side of Equation (19) in turn by Lemma 4, it is easy to obtain…”

Section: The Existence Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…initial conditions and parameter) of solutions, the existence and upper semicontinuity of global attractors, and pullback attractors were obtained, respectively, but the growth exponents depend only on spatial variables. In [19, 20], the authors studied the following nonlinear parabolic equation:

\begin{align} u_t - \text{div} {\left\lbrace |\nabla u|^{p(x)-2} \nabla u\right\rbrace} + f(x,u)=g. \end{align}

First, the existence and fractal dimension of global attractors were obtained.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Upper semicontinuity of pullback D$\mathcal {D}$‐attractors for nonlinear parabolic equation with nonstandard growth condition

Liu

Huang

2023

Mathematische Nachrichten

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“…After that, Bénilan and Boccardo introduced the concept of entropy solution and obtained a unique entropy solution for the nonlinear elliptic problem in [14]. Then, more and more scholars studied renormalized and entropy solutions in elliptic equations (see [15][16][17]) and parabolic equations (see [18][19][20][21][22]). At the same time, many people have made more general equations about Leray-Lions-type operator equations [23][24][25][26][27], anisotropic equations [26,28] and fractional equations [29].…”

Section: Introductionmentioning

confidence: 99%

The Existence of Entropy Solutions for a Class of Parabolic Equations

Chen,

Shen

2023

Mathematics

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The existence and uniqueness of entropy solutions for a class of parabolic equations involving a p(x)-Laplace operator are investigated. We first prove existence of the global weak solution for the p(x)-Laplacian equations with regular initial data via the difference and variation methods as well as the standard domain expansion technique. Then, by constructing and solving a related approximation problem, the entropy solution for the p(x)-Laplacian equations with irregular initial data in whole space is also obtained.

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Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

Niu

Meng

Chai

2020

Applicable Analysis

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Global attractors for nonlinear parabolic equations with nonstandard growth and irregular data

Cited by 6 publications

References 40 publications

Upper semicontinuity of pullback D$\mathcal {D}$‐attractors for nonlinear parabolic equation with nonstandard growth condition

Upper semicontinuity of pullback D$\mathcal {D}$‐attractors for nonlinear parabolic equation with nonstandard growth condition

The Existence of Entropy Solutions for a Class of Parabolic Equations

Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data

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