Source identification for the heat equation

The Semilinear Heat Equation with a Heaviside Source Term

We consider the initial value problem for the equation u t = u xx +H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces .

A note on uniqueness in the identification of a spacewise dependent source and diffusion coefficient for the heat equation

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information from a supplementary temperature measurement at a given single instant of time. In the multi-dimensional case, we use Carleman estimates for parabolic equati...

On source identification problem for a delay parabolic equation∗

Delay parabolic equations (DPEs) have important applications in a wide range of applications such as physics, chemistry, biology and ecology and other fields. For example, diffusion problems where the current state depends upon an earlier one give rise to parabolic equations with delay. In mathematical modeling, DPEs are used together with boundary conditions specifying the solution on the boun...

Solution for the Heat Equation

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given. AMS: 35R30, 80A23