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

  • Marek Fila
  • Johannes LankeitEmail author


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


Mathematics Subject Classification

35K55 35B44 



The first author was supported in part by the Slovak Research and Development Agency under the contract No. APVV-14-0378 and by the VEGA Grant 1/0347/18.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia

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