An Explicit Solution of a Parabolic Equation with Nonlocal Boundary Conditions

We consider a parabolic differential equation with nonlocal boundary conditions. We find an explicit solution of the problem and prove the uniqueness of the solution. Analysis of the explicit solution reveals that it has three physically different linear components. The first component is of standin...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2005-07, Vol.45 (3), Article 257
Main Authors: Bastys, A., Ivanauskas, F., Sapagovas, M.
Format: Article
Language:English
Subjects:
Boundary conditions
Parabolic differential equations
Standing waves
Wave propagation
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Summary:We consider a parabolic differential equation with nonlocal boundary conditions. We find an explicit solution of the problem and prove the uniqueness of the solution. Analysis of the explicit solution reveals that it has three physically different linear components. The first component is of standing wave type, and the other two are of right- and left-going wave types, respectively. The speed of propagation of the heat waves depends on constants present in nonlocal boundary conditions. We give examples of right-going heat waves that have constant energy.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-005-0028-1