Finite time extinction in nonlinear diffusion equations
Laister, R. (2004) Finite time extinction in nonlinear diffusion equations. Applied Mathematics Letters, 17 (5). pp. 561-567. ISSN 0893-9659 Available from: http://eprints.uwe.ac.uk/8187
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Publisher's URL: http://dx.doi.org/10.1016/S0893-9659(04)90126-7
We consider a class of degenerate diffusion equations where the nonlinearity is assumed to be singular (non-Lipschitz) at zero. It is shown that solutions with compactly supported initial data become identically zero in finite time. Such extinction follows by comparison with newly constructed finite travelling waves connecting two stable equilibria.