On a class of nonlinear convolution equations
type: Item
instance of: scholarly article
title: On a class of nonlinear convolution equations
zbMATH Open document ID: 0831.45005
DOI: 10.4171/ZAA/635
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-01-25T00:00:00Z
review text: The main result is an existence and uniqueness statement for operator equations of the second kind \(u + G_0u + G_1 u*G_2u = g\), where \(G_i\) \((i = 0,1,2)\) are Lipschitz continuous operators on either \(L_p (0,T; X)\) or \(C(0,T; X)\), equipped with certain exponentially weighted norms. The proofs are based on the contraction mapping principle. Several corollaries are also given, dealing with generalized versions of the equation above. One motivation for these results comes from an inverse problem, where one tries to identify memory kernels in viscoelasticity and heat transfer. Some further examples involve equations of auto-convolution type, nonlinear stress-strain relations in viscoelasticity, and nonlinear Volterra integro-differential equations.
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45N05
zbMATH DE Number: 800342
zbMATH Keywords: nonlinear convolution equations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: contraction mapping principle
zbMATH Keywords: inverse problem
zbMATH Keywords: memory kernels in viscoelasticity
zbMATH Keywords: heat transfer
zbMATH Keywords: equations of auto-convolution type
zbMATH Keywords: nonlinear stress- strain relations
zbMATH Keywords: nonlinear Volterra integro-differential equations
author: Lothar von Wolfersdorf
author: Jaan Janno
reviewed by: Olof Staffans
MaRDI profile type: Publication
cites work: Inverse problems of memory reconstruction
cites work: Q4114823
cites work: On autoconvolution and regularization
cites work: Global existence for a hyperbolic integrodifferential inverse problem
cites work: Inverse problems for identification of memory kernels in heat flow
cites work: On Identification of Memory Kernels in Linear Viscoelasticity
description: scientific article; zbMATH DE number 800342