On Blowup in Nonlinear Heat Equations
D. Egli, Z. Gang, W. Kong, I. M. Sigal
TL;DR
This paper analyzes the blowup behavior of solutions to nonlinear heat equations with superlinear nonlinearities across various dimensions, providing detailed asymptotic descriptions and remainder estimates.
Contribution
It offers new asymptotic characterizations of blowup solutions and precise remainder estimates for nonlinear heat equations in arbitrary dimensions.
Findings
Derived asymptotic profiles of blowup solutions
Estimated remainders in blowup asymptotics
Applicable to equations with superlinear nonlinearities
Abstract
We establish the asymptotics of blowup for nonlinear heat equations with superlinear power nonlinearities in arbitrary dimensions and we estimate the remainders.
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