Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2002-06-30
A Unified Approach to Nonlinear Integro-Differential Inverse Problems of Parabolic TypeFabio Colombo and D. Guidetti (1) Politecnico di Milano, Italy
(2) Università di Bologna, Italy
We give a unified approach to a class of nonlinear parabolic inverse problems involving kernels of convolution type. Our main tools are optimal regularity results, in Sobolev and H¨older spaces, for parabolic equations and analytic semigroup theory. We apply the main abstract results (Theorems 2.1-2.2) to a model of population dynamics, to the theory of combustion of a material with memory and, finally, to a parabolic equation with elliptic part of order $2m$, which for $m$ = 1 is the heat equation with memory and with non-linearity containg derivatives up to order $2m–1$.
Keywords: Analytic semigroup theory, optimal regularity results, nonlinear parabolic inverse problems
Colombo Fabio, Guidetti D.: A Unified Approach to Nonlinear Integro-Differential Inverse Problems of Parabolic Type. Z. Anal. Anwend. 21 (2002), 431-464. doi: 10.4171/ZAA/1086