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Article information
1996 , Volume 1, ¹ 1, p.13-37
Blokhin A.M., Tkachev D.L.
A mixed problem for the wave equation in coordinate domains.I.Mixed problem for the wave equation in a quadrant
A formal solution from the class to the mixed problem for the classic wave equation in the coordinate corner with boundary conditions of an oblique derivative type is found in the first part of this article. The solution is found for all values of parameters of the boundary conditions such that the Lopatinsky condition is fulfilled on every boundary. The energy inequality (an a priori estimation in ) without loss of generality is proved provided that the right hand sides are finite and the uniform Lopatinsky condition is fulfilled. The second part of this article will be published in the next issue of journal.
[full text] Classificator Msc2000:- *35C05 Solutions in closed form
- 35C15 Integral representations of solutions of PDE
- 35L05 Wave equation
- 35L20 Boundary value problems for second-order, hyperbolic equations
Keywords: mixed boundary value problem, wave equation, integral representation of a solution, a priori estimate
Author(s):
Blokhin Alexander Mikhailovich
Dr. , Professor
Position: Head of Laboratory
Office: Institute of Mathematics SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Koptyug ave, 4
Phone Office: (383) 329 76 75
E-mail: blokhin@math.nsc.ru
Tkachev Dmitriy L
Office: Novosibirsk State University
Address: 630090, Russia, Novosibirsk, Ac. Koptyug ave, 4
Bibliography link:
Blokhin A.M., Tkachev D.L. A mixed problem for the wave equation in coordinate domains.I.Mixed problem for the wave equation in a quadrant // Computational technologies. 1996. V. 1. ¹ 1. P. 13-37
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