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SOLUTION FORMULAS FOR SOME NONLOCAL HEAT EQUATIONS

Huh, Hyungjin

  • Received : 2015.10.28
  • Published : 2016.07.31

Abstract

We obtain solution formulas for some nonlocal heat equations. As a simple application, we prove finite time blow-up of the solution.

Keywords

nonlocal heat equation;solution formula

References

  1. M. Alfaro and R. Carles, Explicit solutions for replicator-mutator equations: extinction versus acceleration, SIAM J. Appl. Math. 74 (2014), no. 6, 1919-1934. https://doi.org/10.1137/140979411
  2. P. Souplet, Gradient blow-up for multidimensional nonlinear parabolic equations with general boundary conditions, Differential Integral Equations 15 (2002), no. 2, 237-256.

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)