Singularity and blow-up estimates via Liouville-type theorems for\n Hardy-H 'enon parabolic equations

2012/10/29 by Quoc Hung Phan, Phan, Quoc Hung · 1 citation
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1210.7722

Abstract

We consider the Hardy-H 'enon parabolic equation u_t-\Δ u =|x|^a\n|u|^p-1u with p>1 and a\∈ mathbb R. We establish the space-time\nsingularity and decay estimates, and Liouville-type theorems for radial and\nnonradial solutions. As applications, we study universal and a priori bound of\nglobal solutions as well as the blow-up estimates for the corresponding initial\nboundary value problem.\n

Citations

• Global and local behavior of positive solutions of nonlinear elliptic equations

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• On blow-up rate for the Hénon parabolic equation with Sobolev supercritical nonlinearity

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