A parabolic inverse problem with an unknown boundary condition
type: Item
instance of: scholarly article
title: A parabolic inverse problem with an unknown boundary condition
zbMATH Open document ID: 0705.35150
DOI: 10.1016/0022-0396(90)90031-J
author: William Rundell
author: Hong-Ming Yin
published in: Journal of Differential Equations
publication date: 1990-01-01T00:00:00Z
review text: Die Verfasser untersuchen das folgende parabolische inverse Problem, bei dem eine unbekannte Funktion \(p(s)\) in den Randbedingungen auftritt, die durch Messung der Temperatur \(u(x,t)\) in einem festen Punkt \(x_ 0\) des Randes ermittelt werden soll: \[ u_ t-\Delta u=f(x,t),\quad (x,t)\in \Omega \times (0,T],\quad \Omega \subset {\mathbb{R}}^ n, \] \[ \partial u/\partial N+p(u)=g(x,t)\text{ auf }\partial \Omega \times [0,T], \] \[ u(x,0)=u_ 0(x)\text{ auf }{\bar \Omega},\quad u(x_ 0,t)=h(t)\text{ für }t\in [0,T],\quad x_ 0\in \partial \Omega. \] Die gesuchte Funktion p sei definiert in dem Intervall \([\min u, \max u]\), wenn \((x,t)\) aus \({\bar \Omega}\times [0,T].\) Unter geeigneten Voraussetzungen über g und h zeigen die Verfasser, daß es höchstens eine Lösung im klassischen Sinn gibt.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 4157150
zbMATH Keywords: unknown boundary condition
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
cites work: A uniqueness theorem for a class of nonlinear parabolic inverse problems
cites work: A class of nonlinear non-classical parabolic equations
cites work: Unicity in an inverse problem for an unknown reaction term in a reaction- diffusion equation
cites work: Q5520962
cites work: Geometric theory of semilinear parabolic equations
cites work: An inverse problem for a semilinear parabolic equation
cites work: Uniqueness theorems for some converse problems of heat conduction
cites work: Unique Identification of Eigenvalues and Coefficients in a Parabolic Problem
cites work: An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problem
cites work: Restoration of the boundary condition in the boundary value problem for the heat equation
cites work: On the inverse problem for the quasilinear equation of thermal conductivity
cites work: Remarks on the uniqueness in an inverse problem for the heat equation. I
cites work: Remarks on the uniqueness in an inverse problem for the heat equation. II
cites work: Q3721086
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description: scientific article; zbMATH DE number 4157150