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Selçuk Journal
of
Applied Mathematics
Summer-Autumn, 2000
Volume 1
Number 1
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2000, Volume 1 - Number 1
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The Cauchy problem for pseudohyperbolic equations
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Gennadii Demidenko* |
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Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia
email: demidenk@math.nsc.ru
Received: 15.02. 2000
To
Prof. Dr. Chr. Zenger 60-th birthday
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Summary
In this paper we study the Cauchy problem for a class of partial differential equations not solved with respect to the highest derivative. The members of this class are called pseudohyperbolic equations. We establish the solvability conditions, obtain an ``energy" inequality for solutions, and prove the well-posedness of the Cauchy problem in the weighted Sobolev spaces. |
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Key
words
equations not solved with respect to the highest derivative, the
weighted Sobolev spaces, the Cauchy problem, pseudohyperbolic
equations
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Mathematics Subject Classification (1991):
35M05,
35M20.
*
The research was financially supported by the Russian Foundation for
Basic Research (No. 98-01-00553, No. 99-01-00533) and by the
Ministry of general and professional education of the Russian
Federation.
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Article
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Article in ZIP
format (60 kb) |
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