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Hölder space solutions of free boundary problems that arise in combustion theory

Author: G. I. Bizhanova
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 27 (2015), nomer 2.
Journal: St. Petersburg Math. J. 27 (2016), 207-235
MSC (2010): Primary 35R35
Published electronically: January 29, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: Multidimensional single-phase problems with free boundary are studies for the heat equation with derivative in the direction of the gradient of the unknown function in differential equations on the free boundary. The unique solvability of such problems is established in Hölder spaces for small times, and coercive estimates are obtained for the solutions.

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Additional Information

G. I. Bizhanova
Affiliation: Institute of Mathematics and Mathematical Modeling, Pushkin str. 125, Almaty, Kazakhstan

Keywords: Free boundary problems, heat equation, H\"older spaces, unique solvability, coercive estimates for solutions
Received by editor(s): October 10, 2014
Published electronically: January 29, 2016
Dedicated: Dedicated to Professor Vsevolod Alekseevich Solonnikov on the occasion of his anniversary
Article copyright: © Copyright 2016 American Mathematical Society