Existence and Uniqueness of the Solution of a Mixed Problem for a Parabolic Equation Under Nonconventional Boundary Conditions

Abstract

Our research focuses on examining a mixed problem associated with a second-order parabolic equation that features temporal mixing and variable coefficients, subject to non-local and non-self-adjoint boundary conditions. We establish the problem’s unique solvability by imposing specific conditions on the provided data, utilizing a combination of residue and contour integral methods. Additionally, our study produces an explicit analytical solution for addressing the problem at hand.