Blow-up Rate Estimates for a Semilinear Heat Equation with a Gradient Term
Maan A. Rasheed, Miroslav Chlebik
TL;DR
This paper investigates the blow-up behavior and rate estimates of solutions to a semilinear heat equation with a gradient term under zero Dirichlet boundary conditions.
Contribution
It provides new pointwise and blow-up rate estimates for solutions to a semilinear heat equation with a gradient term, enhancing understanding of their blow-up dynamics.
Findings
Derived pointwise estimates for solutions.
Established blow-up rate estimates.
Analyzed the effects of the gradient term on blow-up behavior.
Abstract
We consider the the pointwise estimates and the blow-up rate estimates for the zero Dirchilet problem of the semilinear heat equation with a gradient term.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations