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Asymptotics of solutions of the heat equation in cones and dihedra under minimal assumptions on the boundary

Vladimir A Kozlov1 and Jürgen Rossmann2*

Author Affiliations

1 Institute of Mathematics, Linköping University, Linköping, SE-58183, Sweden

2 Institute of Mathematics, University of Rostock, Rostock, D-18051, Germany

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Boundary Value Problems 2012, 2012:142  doi:10.1186/1687-2770-2012-142

Published: 3 December 2012

Abstract

In the first part of the paper, the authors obtain the asymptotics of Green’s function of the first boundary value problem for the heat equation in an m-dimensional cone K. The second part deals with the first boundary value problem for the heat equation in the domain <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M1">View MathML</a>. Here the right-hand side f of the heat equation is assumed to be an element of a weighted <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M2">View MathML</a>-space. The authors describe the behavior of the solution near the <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/142/mathml/M3">View MathML</a>-dimensional edge of the domain.