• 대한수학회논문집
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• 제36권3호
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• pp.447-463
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• 2021

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

• 대한수학회논문집
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• 제37권2호
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.

• 대한수학회보
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• 제51권5호
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• pp.1299-1324
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• 2014

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.