Global solutions of the fast diffusion equation with gradient absorption terms
In the present study the authors consider the Cauchy problem of the fast diffusion equation with nonlinear gradient absorption terms \[ u_t-\Delta(u^m)+ |\nabla u|^p=0\text{ in }\mathbb{R}^d\times(0,\infty)\quad u(x,0)=u_0(x)\text{ in } \mathbb{R}^d, \] where \(1<p<2\) and \((1-\frac 2d)^+<m<1\). The authors also study the large time behaviour of the \(L^1\)-norm of solutions.
scientific article; zbMATH DE number 5083589
scientific article