Sharp estimates and finite speed of propagation for a Neumann problem in domains narrowing at infinity. (English) Zbl 0987.35090

The authors study the connection between the geometry of an unbounded domain and existence and qualitative behavior of solutions to a degenerate doubly nonlinear parabolic equation posed in the domain. The domain is assumed to be “narrowing” at infinity in a suitable sense and possessed homogeneous Neumann condition. The authors also show that even if the initial datum has initial mass, the solution need not be globally bounded over the domain for a fixed positive time.
Reviewer: Jiaqi Mo (Wuhu)


35K65 Degenerate parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K55 Nonlinear parabolic equations