Continuation beyond interior gradient blow-up in a semilinear parabolic\n equation

2019/02/04 by Марек Фила, Fila, Marek, Johannes Lankeit +1
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.1902.01127

Abstract

It is known that there is a class of semilinear parabolic equations for which\ninterior gradient blow-up (in finite time) occurs for some solutions. We\nconstruct a continuation of such solutions after gradient blow-up. This\ncontinuation is global in time and we give an example when it never becomes a\nclassical solution again.\n

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