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Asymptotics of solutions of second order parabolic equations near conical points and edges
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
University of Rostock, Germany.
2014 (English)In: Boundary Value Problems, ISSN 1687-2762, E-ISSN 1687-2770, no 252Article in journal (Refereed) Published
Abstract [en]

The authors consider the first boundary value problem for a second order parabolic equation with variable coefficients in a domain with conical points or edges. In the first part of the paper, they study the Green function for this problem in the domain K x Rn-m, where K is an infinite cone in R-m, 2 less than= m less than= n. They obtain the asymptotics of the Green function near the vertex ( n = m) and edge ( n greater than m), respectively. This result is applied in the second part of the paper, which deals with the initial-boundary value problem in this domain. Here, the right-hand side f of the differential equation belongs to a weighted L-p space. At the end of the paper, the initial-boundary value problem in a bounded domain with conical points or edges is studied.

Place, publisher, year, edition, pages
Hindawi Publishing Corporation / Springer Verlag (Germany) / SpringerOpen , 2014. no 252
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URN: urn:nbn:se:liu:diva-114020DOI: 10.1186/s13661-014-0252-xISI: 000347398000001OAI: diva2:786492
Available from: 2015-02-05 Created: 2015-02-05 Last updated: 2015-02-24

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Kozlov, Vladimir
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