Recovery of a Rapidly Oscillating Source in the Heat Equation from Solution Asymptotics

Resumo

Four problems are solved in which a high-frequency source in the one-dimensional heat equation with homogeneous initial–boundary conditions is recovered from partial asymptotics of its solution. It is shown that the source can be completely recovered from an incomplete (two-term) asymptotic representation of the solution. The formulation of each source recovery problem is preceded by constructing and substantiating asymptotics of the solution to the original initial–boundary value problem.