Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type
The authors study global existence and nonexistence of solutions of abstract quasilinear evolution problems involving potential operators. Using energy methods, they show nonexistence of global solutions provided the energy of the initial function is negative (or \(\ll0\)). The global existence result is based on suitable structure conditions on the corresponding potentials. The abstract theory is illustrated by examples of the type \(|u_t|^{m-2}u_t-a\nabla\cdot(|\nabla u|^{q-2}\nabla u)=|u|^{p-2}u\).
abstract quasi-linear evolution problems
scientific article; zbMATH DE number 1130548
scientific article