Existence and multiplicity of blow-up profiles for a quasilinear
diffusion equation with source
Existence and multiplicity of blow-up profiles for a quasilinear
diffusion equation with source
We classify radially symmetric self-similar profiles presenting finite time blow-up to the quasilinear diffusion equation with weighted source $$ u_t=\Delta u^m+|x|^{\sigma}u^p, $$ posed for $(x,t)\in\real^N\times(0,T)$, $T>0$, in dimension $N\geq1$ and in the range of exponents $-2<\sigma<\infty$, $1<m<p<p_s(\sigma)$, where $$ p_s(\sigma)=\left\{\begin{array}{ll}\frac{m(N+2\sigma+2)}{N-2}, & N\geq3,\\ +\infty, & N\in\{1,2\},\end{array}\right. $$ is the renowned Sobolev …