The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (316 KB) | Metadata | Table of Contents | ZAA summary
Volume 21, Issue 2, 2002, pp. 431–464
DOI: 10.4171/ZAA/1086

Published online: 2002-06-30

A Unified Approach to Nonlinear Integro-Differential Inverse Problems of Parabolic Type

Fabio Colombo[1] and D. Guidetti[2]

(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