Blow-up Rate Estimates for Parabolic Equations
Maan A. Rasheed, Miroslav Chlebik
TL;DR
This paper investigates the behavior of solutions to certain parabolic equations, focusing on the blow-up sets and deriving upper estimates for the rate at which solutions become unbounded.
Contribution
It introduces new methods for estimating blow-up rates and characterizes blow-up sets for specific parabolic problems in a ball.
Findings
Identified conditions for blow-up in parabolic equations
Derived upper bounds for blow-up rates
Characterized blow-up sets in radial domains
Abstract
We consider the blow-up sets and the upper blow-up rate estimates for two parabolic problems defined in a ball.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Stability and Controllability of Differential Equations · Advanced Mathematical Physics Problems