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Diffusivity versus absorption through the boundary. (English) Zbl 0761.35048

In the rectangle \(0<x<1\), \(0<t<T\), the equation \((u^ m)_ t- u_{xx}=0\) is considered with positive given initial \(u\) and boundary conditions \(u_ x(0,t)=0\), \(u_ x(1,t)=u(1,t)\). The aim of the article is to extend to the general case \(m>0\) the results (of global solvability and blow up in finite time) already known for the heat equation \((m=1)\).

MSC:

35K57 Reaction-diffusion equations
35Q35 PDEs in connection with fluid mechanics
35K15 Initial value problems for second-order parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
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