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.
Izv. Akad. Nauk SSSR. Ser. Mat., 18, 3–50 (1954)
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References
Sobolev, S. L.: Some Applications of Functional Analysis in Mathematical Physics. Izdat. Leningrad. Gosudarstv. Univ., Leningrad (1950)
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Sobolev, S.L. (2006). On a New Problem of Mathematical Physics. In: Demidenko, G.V., Vaskevich, V.L. (eds) Selected Works of S.L. Sobolev. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34149-1_9
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DOI: https://doi.org/10.1007/978-0-387-34149-1_9
Publisher Name: Springer, Boston, MA
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