Operational calculus approach to PDE arising in QR-regularisation of ill-posed problems
The authors treat two kinds of problems using operational calculus intended for boundary value problems: the first for the backward heat equation, and the second for a nonparabolic evolution equation. They discuss the algebraization of the boundary value problem using the Duhamel principle and obtain their solution in closed form. Ill-posed problems for linear partial differential equations are replaced by well-posed problems for equations of twice-higher order in the method of quasi-reversibility.
scientific article; zbMATH DE number 1781842