Convergence to a stationary state for solutions to parabolic inverse problems of reconstruction of convolution kernels. (English) Zbl 1212.35501

Summary: 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.


35R30 Inverse problems for PDEs
35B20 Perturbations in context of PDEs
35K90 Abstract parabolic equations