Strong pullback attractors for a nonclassical diffusion equation
Xiaolei Dong,Yuming Qin +1 more
TL;DR: In this article , the authors investigated the existence of pullback attractors for a non-classical diffusion equation with Dirichlet boundary condition and proved the existence and uniqueness of strong solutions.
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Abstract: <p style='text-indent:20px;'>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.</p>
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Citations
Strong global attractors for a three dimensional nonclassical diffusion equation with memory
Yuming Qin,Xiaolei Dong,Alain Miranville,Ke Wang +3 more
- 31 Mar 2023
TL;DR: In this paper , the authors studied the strong global attractors for a three dimensional nonclassical diffusion equation with memory and proved the existence and uniqueness of strong solutions for the equations by the Galerkin method.
1
Pullback D$$ \mathcal{D} $$ ‐attractors for doubly nonlinear parabolic equations
Yongjun Li,Li Chen +1 more
TL;DR: In this paper , a class of doubly nonlinear parabolic equations (1.1) is studied and the authors prove that the process corresponding to the problem is norm-to-weak continuous.
References
Attractors for reaction-diffusion equations in unbounded domains
TL;DR: In this article, the asymptotic behavior of solutions for parabolic non-linear evolution equations in R n is studied and the existence of the global attractor in L 2 (R n ) is established.
322
The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations
TL;DR: In this paper, the existence of the global attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term was verified.
268
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems
TL;DR: In this article, a new explicit algorithm allowing us to construct exponential attractors which are uniformly and continuous with respect to the variation of the dynamical system in some natural large class is proposed.
146
Dynamics of the nonclassical diffusion equations
Chunyou Sun,Meihua Yang +1 more
TL;DR: The dynamical behavior of the nonclassical diffusion equation with critical nonlinearity for both autonomous and nonautonomous cases is considered and the existence of a compact uniform attractor together with its structure and regularity is obtained.
113
Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction–diffusion equations
Yongjun Li,Chengkui Zhong +1 more
TL;DR: The concept of norm-to-weak continuous process in a Banach space is introduced, and the existence of pullback attractors for nonautonomous reaction–diffusion equation in H 0 1 with exponential growth of the external force is obtained.
94