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Regularity of the solution of the Cauchy problem for a higher-order parabolic equation

Regularity of the solution of the Cauchy problem for a higher-order parabolic equation We prove the unique solvability of the Cauchy problem in a weighted Hölder space for a linear parabolic equation of order 2m under the condition that the lower coefficients and the right-hand side of the equation can have certain growth when approaching the plane that is the support of the initial data, while the higher coefficients do not necessarily satisfy the Dini condition near this plane. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Regularity of the solution of the Cauchy problem for a higher-order parabolic equation

Differential Equations , Volume 46 (4) – Jun 3, 2010

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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266110040105
Publisher site
See Article on Publisher Site

Abstract

We prove the unique solvability of the Cauchy problem in a weighted Hölder space for a linear parabolic equation of order 2m under the condition that the lower coefficients and the right-hand side of the equation can have certain growth when approaching the plane that is the support of the initial data, while the higher coefficients do not necessarily satisfy the Dini condition near this plane.

Journal

Differential EquationsSpringer Journals

Published: Jun 3, 2010

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