In this paper, we study the strong global attractors for a three dimensional nonclassical diffusion equation with memory. First, we prove the existence and uniqueness of strong solutions for the equations by the Galerkin method. Then we prove the existence of global attractors for the equations in $H^2(\Omega)\cap H^1_0(\Omega)\times L^2_\mu(\mathbb{R}^+;H^2(\Omega)\cap H^1_0(\Omega))$ by the condition (C).

Strong global attractors for a three dimensional nonclassical diffusion equation with memory

In this paper, we study a class of doubly nonlinear parabolic equations (1.1). The nonlinearity β(u)$$ \beta (u) $$ brings great difficulties to the study of the problem. First, we show that the problem has a unique solution. Then, we prove that the process corresponding to the problem is norm‐to‐weak continuous. After that, by using Legendre transform, we obtain uniform estimates and asymptotic compactness properties that allow us to ensure the existence of pullback D$$ \mathcal{D} $$ ‐attractors for the associated process to the problem.

Pullback 
 D$$ \mathcal{D} $$ ‐attractors for doubly nonlinear parabolic equations

In this paper, we discuss the long-time behavior of solutions to the nonclassical diffusion equation with fading memory when the nonlinear term $f$ fulfills the polynomial growth of arbitrary order and the external force $ g(x)\in L^{2}(\Omega)$. In the framework of time-dependent spaces, we verify the existence and uniqueness of strong solutions by the Galerkin method, then we obtain the existence of the time-dependent global attractor $\mathscr{A}=\{A_t\}_{t\in \mathbb{R}}$ in $\mathcal{M}_t^1$.

Strong attractors for the nonclassical diffusion equation with fading memory in time-dependent spaces

In this paper, we investigate the existence of pullback attractors for a nonclassical diffusion equation with Dirichlet boundary condition in <inline-formula><tex-math id="M1">\begin{document}$ H^2(\Omega)\cap H^1_0(\Omega) $\end{document}</tex-math></inline-formula>. First, we prove the existence and uniqueness of strong solutions for a nonclassical diffusion equation. Then we prove the existence of pullback attractors in <inline-formula><tex-math id="M2">\begin{document}$ H^2(\Omega)\cap H^1_0(\Omega) $\end{document}</tex-math></inline-formula> by applying asymptotic a priori estimate method.

https://www.aimsciences.org/article/exportPdf?id=98094b18-4010-43fe-9cc1-c27ecba196b2

Strong pullback attractors for a nonclassical diffusion equation

<abstract>In this paper, we investigate the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $. First, we prove the existence of pullback attractors for a nonclassical diffusion equation with arbitrary polynomial growth condition by applying the operator decomposition method. Then, by the fractal dimension theorem of pullback attractors given by [<xref ref-type="bibr" rid="b6">6</xref>], we prove the finite fractal dimension of pullback attractors for a nonclassical diffusion equation in $ H^1_0(\Omega) $.</abstract>

Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of {limit} columns in the table. Remove at least 1 column to add or create another one.

Xiaolei Dong

Author Tools

Chat about Author

Papers

Strong pullback attractors for a nonclassical diffusion equation

Finite fractal dimension of pullback attractors for a nonclassical diffusion equation

Strong global attractors for a three dimensional nonclassical diffusion equation with memory