Blowup of solutions for nonlinear nonlocal heat equations
Piotr Biler
TL;DR
This paper investigates the conditions under which solutions to a nonlinear nonlocal heat equation blow up in finite time, providing a dichotomy that distinguishes between global existence and blowup scenarios.
Contribution
It introduces a new blowup analysis framework for nonlocal heat equations with localized sources, extending previous results on global solutions.
Findings
Established criteria for finite-time blowup.
Identified conditions for global existence.
Provided a dichotomy between blowup and global solutions.
Abstract
Blowup analysis for solutions of a general evolution equation with nonlocal diffusion and localized source is performed. By comparison with recent results on global-in-time solutions, a dichotomy result is obtained.
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Taxonomy
TopicsFractional Differential Equations Solutions · Stability and Controllability of Differential Equations · Advanced Mathematical Physics Problems