On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures

Abstract

Considering a mixed boundary-value problem for a non-linear heat equation with the nonhomogeneous Neumann condition, the right-hand side and the initial condition in space of sign-measures, we establish large-data existence results even if the convective term is not integrable.

Keywords

• solvability
• non-linear heat equation
• non-integrable convective term
• measures