Semilinear Heat Models

Marcelo R. Ebert and Michael Reissig
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Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 17 in Methods for Partial Differential Equations, 2018, pp 273-297 from Springer

Abstract: Abstract In this chapter we consider the semilinear heat model with power nonlinearity u t − Δ u = ± | u | p − 1 u , u ( 0 , x ) = φ ( x ) . $$\displaystyle {u_t} - \varDelta u =\pm |u|^{p-1}u,\,\,\,u(0,x)=\varphi (x).$$ Here ±|u| p−1 u is an example of a source nonlinearity (positive sign) and of an absorbing nonlinearity (negative sign) (see, for example, [153]).

Date: 2018
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DOI: 10.1007/978-3-319-66456-9_17

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