## Differential and Integral Equations

### Convergence to a stationary state for solutions to parabolic inverse problems of reconstruction of convolution kernels

Davide Guidetti

#### Abstract

We prove the existence of solutions converging to a stationary state for abstract semilinear parabolic problems with a convolution kernel that is unknown (together with the solution). These solutions are suitable perturbations of stationary states. The main tools are maximal regularity results in an $L^1$ (time) setting. The abstract results are applied to a reaction-diffusion integrodifferential system.

#### Article information

Source
Differential Integral Equations Volume 20, Number 9 (2007), 961-990.

Dates
First available in Project Euclid: 20 December 2012