Global nonexistence for a quasilinear evolution equation with a generalized Lewis function
Summary: We consider the following quasilinear parabolic equation \[ a(x,t)u_t-\text{div}\bigl(|\nabla u|^{m-2}\nabla u\bigr)=f(u), \] where \(a(x,t)\geq 0\) is a generalized Lewis function. The main result is that the solution blows up in finite time if the initial datum \(u(x,0)\) possesses suitable positive energy. Moreover, we have a precise estimate for the lifespan of the solution in this case. Blow up of solutions with vanishing initial energy is considered, too.
scientific article; zbMATH DE number 2186776