Singular Phenomena of Solutions for Nonlinear Diffusion Equations involving $p(x)$-\hbox{Laplacian} Operator

Bin Guo; Wenjie Gao

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arXiv · 1308.2466

Singular Phenomena of Solutions for Nonlinear Diffusion Equations involving $p(x)$-\hbox{Laplacian} Operator

Bin Guo·Wenjie Gao

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Abstract

The authors of this paper study singular phenomena(vanishing and blowing-up in finite time) of solutions to the homogeneous $\hbox{Dirichlet}$ boundary value problem of nonlinear diffusion equations involving $p(x)$-\hbox{Laplacian} operator and a nonlinear source. The authors discuss how the value of the variable exponent $p(x)$ and initial energy(data) affect the properties of solutions. At the same time, we obtain the critical extinction and blow-up exponents of solutions.

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BibTeX RIS

Bin Guo, Wenjie Gao. 2013-08-12. Singular Phenomena of Solutions for Nonlinear Diffusion Equations involving $p(x)$-\hbox{Laplacian} Operator. https://arxiv.org/abs/1308.2466

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