Selšuk Journal of Applied Mathematics

 Selšuk Journal of
  Applied Mathematics

  Summer-Autumn, 2000
  Volume  1
  Number 1

Research Center of 
  Applied Mathematics

 SJAM Summer-Autumn 2000, Volume 1 - Number 1

The Cauchy problem for pseudohyperbolic equations

Gennadii Demidenko*

Sobolev Institute of Mathematics, SB RAS, Novosibirsk, Russia


Received: 15.02. 2000

To Prof. Dr. Chr. Zenger 60-th birthday

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.


Key words
equations not solved with respect to the highest derivative, the weighted Sobolev spaces, the Cauchy problem, pseudohyperbolic equations

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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