On positive solutions of the heat equation satisfying a nonlinear boundary condition

We consider a boundary value problem for the heat equation in the exterior of a bounded domain of space variables. On the boundary of the domain, we pose a nonlinear boundary condition. We find sharp nonlinearity exponents for which there exists no global solution.

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Bibliographic Details
Published in:	Differential equations Vol. 46; no. 8; pp. 1114 - 1122
Main Author:	Kondrat’ev, V. A.
Format:	Journal Article
Language:	English
Published:	Dordrecht SP MAIK Nauka/Interperiodica 01-08-2010 Springer Nature B.V
Subjects:	Boundaries Boundary conditions Boundary value problems Cauchy problems Difference and Functional Equations Differential equations Exteriors Heat equations Mathematical analysis Mathematics Mathematics and Statistics Nonlinear systems Nonlinearity Ordinary Differential Equations Partial Differential Equations Studies Cauchy Problem Global Solution Maximum Principle Heat Equation Bounded Domain
Online Access:	Get full text
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Description
Summary:	We consider a boundary value problem for the heat equation in the exterior of a bounded domain of space variables. On the boundary of the domain, we pose a nonlinear boundary condition. We find sharp nonlinearity exponents for which there exists no global solution.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266110080057