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On the existence and uniqueness of a generalized solution of the Protter problem for (3 + 1) -D Keldysh-type equations

Popivanov, N.; Hristov, T.; Nikolov, A.; Schneider, M.

Abstract: A (3+1)-dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi type (the first kind) or for the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues of Darboux or Cauchy-Goursat plane problems. Now, it is well known that Protter problems are not correctly set, and they have singular generalized solutions, even for smooth right-hand sides. In this paper an analogue of the Protter problem for equations of Keldysh type is given. An appropriate generalized solution with possible singularity is defined. Results for uniqueness and existence of such a generalized solution are obtained. Some a priori estimates are stated.

Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2017
Sprache Englisch
Identifikator DOI: 10.1186/s13661-017-0757-1
ISSN: 1687-2762, 1687-2770
KITopen ID: 1000067271
Erschienen in Boundary value problems
Band 2017
Heft 1
Seiten 26
Schlagworte weakly hyperbolic equations, boundary value problems, generalized solutions, uniqueness, behavior of solution
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