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Abstract

Abstract:

In this paper, we study the long-time dynamical behavior of solutions for the nonclassical diffusion equation with time-dependent memory kernel in the time-dependent space $H_{0}^1(\Omega)\times L_{\mu_{t}}^2(\mathbb R^+; H_{0}^1(\Omega))$. Under the new theorical framework, the well-posedness of the solution, the existence and the regularity of the time-dependent global attractors are proved by using the delicate integral estimation method and decomposition technique.

Key words: Nonclassical diffusion equation, Time-dependent memory kernel, Well-posedness, Time-dependent global attractors, Regularity of the attractors

CLC Number:

O175.29

Wang Xuan, Yuan Haiyan. Attractors for the Nonclassical Diffusion Equation with Time-Dependent Memory Kernel[J].Acta mathematica scientia,Series A, 2024, 44(2): 429-452.

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References

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Attractors for the Nonclassical Diffusion Equation with Time-Dependent Memory Kernel

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