Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term. (English) Zbl 1295.35294
Summary: We study the Cauchy problem for the degenerate and uniformly parabolic equations with gradient term. The local existence, global existence and non-existence of solutions are obtained. In the case of global solvability, we get the exact estimates of a solution. In particular, we obtain the global existence of solutions in the limiting case.
MSC:
35K92 | Quasilinear parabolic equations with \(p\)-Laplacian |
35K65 | Degenerate parabolic equations |
35B44 | Blow-up in context of PDEs |