Title: Initial-Boundary Value Problem for a Heat Equation with not Strongly Regular Boundary Conditions
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.
Publication Year: 2017
Publication Date: 2017-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 5
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