On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources
The existence of solutions to the problem \[ u_t= \text{div}(|\nabla u^m|^{p-2}\nabla u^m)+ {u^q\over(1+|x|)^\alpha},\qquad u(x,0)= u_0(x) \] is considered in \(\mathbb{R}^n\times (0,T]\). Here \(p> 2\), \(m> 1\), \(q> 1\) but \(\alpha\) is arbitrary. The results include some quantitative estimates.
scientific article; zbMATH DE number 5643343