Degenerate quasilinear parabolic problems with slow diffusions (Q2754429)

The article is devoted to studying the following degenerate parabolic problem NEWLINE\[NEWLINE \begin{gathered} x^q\nu_t = m\nu^{(m-1)/m}v_{xx} + m\nu^{(p+m-1)/m} \quad\text{in }\Omega_T,\\ \nu(x,0) = \nu_0(x) \quad \text{on } \overline D,\\ \nu(0,t) = 0 = \nu(1,t) \quad \text{for } t \in (0,T), \end{gathered} NEWLINE\]NEWLINE where \(\nu = u^m\) with \(u\) denoting the particle density. The authors show the existence of a classical solution of the problem and also discuss the location of the blow-up point.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].