Geodesic
The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 193-199
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Some three-dimensional analogues of the plane Darboux problems for weakly hyperbolic equations are studied. In 1952 M. Protter formulated new 3-D boundary value problems for a class of weakly hyperbolic equations, as well as for some hyperbolic- elliptic equations. In the contrast of the well-posedness of the Darboux problem in 2-D case, the new problems are strongly ill-posed. For weakly hyperbolic equation, involving lower order terms, we find sufficient conditions for existence and uniqueness of generalized solutions with isolated power-type singularities as well as for uniqueness of quasi-regular solutions to the Protter problem. *2000 Mathematics Subject Classification: 35L20, 35A20.
Keywords: Weakly Hyperbolic Equations, Boundary Value Problems, Generalized Solutions, Quasi-Regular Solutions, Singular Solutions 
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Popivanov, Nedyu; Hristov, Tsvetan. The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 193-199. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a17/