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On a New Problem of Mathematical Physics

In: Selected Works of S.L. Sobolev

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  • S. L. Sobolev

Abstract

Summary We consider a system of partial differential equations that is not a Kovalevskaya system. The Cauchy problem and the mixed problem in a smooth domain are studied. We prove the existence of a solution in a Hilbert space H and the continuous dependence on the initial conditions. The Cauchy problem in an unbounded space is solved explicitly.

Suggested Citation

  • S. L. Sobolev, 2006. "On a New Problem of Mathematical Physics," Springer Books, in: Gennadii V. Demidenko & Vladimir L. Vaskevich (ed.), Selected Works of S.L. Sobolev, chapter 9, pages 279-332, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-34149-1_9
    DOI: 10.1007/978-0-387-34149-1_9
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