An inverse problem in the theory of combustion of materials with memory
type: Item
instance of: scholarly article
title: An inverse problem in the theory of combustion of materials with memory
zbMATH Open document ID: 0958.35145
author: Fabrizio Colombo
author: Alfredo Lorenzi
published in: Advances in Differential Equations
publication date: 2001-03-27T00:00:00Z
review text: The authors study the following inverse problem in a Banach space \(X\): Find the functions \(h,u\) and \(\rho\) from the relations \[ u'(t)=Au(t)+\int_0^t h(t-s)Au(s) ds+f(u(t),\rho(t)),\quad t\in [0,T], \] \[ \rho'(t)=B\rho(t)+g(u(t),\rho(t)),\quad t\in[0,T], \] \[ u(0)=u_0,\quad \rho(0)=\rho_0, \qquad \Phi(u(t))=\ell(t), \quad t\in[0,T], \] where \(A\) and \(B\) are linear closed operators with dense domains, and \(\Phi\) is a linear bounded functional on \(X\). Using a fixed point theorem the authors prove the local (with respect to \(t\)) solvability of the inverse problem. Then, this result is applied to prove local solvability of the inverse problem with integral overdetermination for a system of combustion equations having a convolution term which describes the thermal memory of the material.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 45G15
Mathematics Subject Classification ID: 45N05
zbMATH DE Number: 1449011
zbMATH Keywords: local solvability
zbMATH Keywords: integral overdetermination
zbMATH Keywords: combustion equations
zbMATH Keywords: thermal memory
reviewed by: V. A. Yurko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1449011