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Self-Similar Subsolutions and Blowup for Nonlinear Parabolic Equations

Self-similar subsolutions and blow-up for nonlinear parabolic equations
Authors: Souplet, Philippe; Weissler, Fred B;

Self-Similar Subsolutions and Blowup for Nonlinear Parabolic Equations

Abstract

Summary: For a wide class of nonlinear parabolic equations of the form \(u_t-\Delta u=F(u, \nabla u)\), we give finite time blow-up results for large initial data. Blow-up time estimates are also provided. These results rely on a new method of comparison with suitable blowing up self-similar subsolutions. As a consequence, we improve several known results on reaction-diffusion equations, on generalized Burgers' equations and on the equation of Chipot and Weissler. This method can also apply to degenerate equations of porous medium type, and provides a unified treatment for a large class of problems, both semilinear and quasilinear.

Keywords

blow up times, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, Applied Mathematics, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, large initial data, Maximum principles in context of PDEs, degenerate equations of porous medium type, equation of Chipot and Weissler, Nonlinear parabolic equations, gradient term, generalized Burgers' equations, Stability in context of PDEs, Analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Top 10%
Top 10%
Top 10%
hybrid