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On Evolution of Invariant Riemannian MetricsRiemannian metric onGeneralized wallach space Generalized Wallach SpacesWallach space Under the Normalized Ricci FlowNormalized Ricci flow Read chapter Read first chapter

2017 | OriginalPaper | Chapter

Initial-Boundary Value Problem for a Heat Equation with not Strongly Regular Boundary Conditions

Author : Makhmud A. Sadybekov

Published in: Functional Analysis in Interdisciplinary Applications

Publisher: Springer International Publishing

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Abstract

We consider a problem on finding a solution of an initial-boundary value problem for a heat equation with regular, but not strongly regular boundary conditions. It is shown that in the case of the potential parity \(q(x)=q(1-x)\) the researched class of problems can always be reduced to a sequential solution of two analogous problems, but with strongly regular boundary conditions. Herewith the proof does not depend on whether the system of eigen- and associated functions of a corresponding spectral problem for an ordinary differential equation arising in applying the Fourier method forms a basis. The suggested way of the problem solution can be applied for constructing as classical, and for various types of generalized solutions. The solution method earlier suggested by the author is modernized. Due to this fact input data of the problem do not require an additional smoothness.

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previous chapter Isoperimetric Inequalities for Some Integral Operators Arising in Potential Theory
next chapter On S-Number Inequalities of Triangular Cylinders for the Heat Operator
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Metadata
Title
Initial-Boundary Value Problem for a Heat Equation with not Strongly Regular Boundary Conditions
Author
Makhmud A. Sadybekov
Copyright Year
2017
Book
Functional Analysis in Interdisciplinary Applications

Print ISBN: 978-3-319-67052-2

Electronic ISBN: 978-3-319-67053-9

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-67053-9_32

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