Diffusivity versus absorption through the boundary
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 \((m=1)\).
scientific article; zbMATH DE number 93318
scientific article