On critical exponents for the heat equation with a mixed nonlinear Dirichlet-Neumann boundary condition
The heat equation in an unbounded domain is considered. On a part of the boundary, a nonlinear Neumann boundary condition is imposed and on another part, the homogeneous Dirichlet boundary condition holds. Critical exponents for the existence of global positive solutions are found for a sectorial domain in the plane and for an \(n\)-dimensional orthant domain.
homogeneous Dirichlet boundary condition
scientific article; zbMATH DE number 1031629
scientific article