Autors: Nikolov, A. Y.
Title: Explicit Solutions of Protter’s Problem for a 4-D Hyperbolic Equation Involving Lower Order Terms with Constant Coefficients
Keywords: singular solutions, Protters problem

Abstract: The Protter’s problems are multidimensional variants of the 2-D Darboux problems for hyperbolic and weakly hyperbolic equations and they are not well-posed in the frame of classical solvability, since their adjoint homogeneous problems have infinitely many nontrivial classical solutions. The generalized solutions of the Protter’s problem may have strong singularities even for very smooth right-hand side functions of the equation. These singularities are isolated at one boundary point and do not propagate along the bicharacteristics which is unusually for the hyperbolic equations. Here we treat a generalization of the well studied Protter’s problem for the 4-D wave equation, considering a case of more general equation involving lower order terms with constant coefficients. First, we announce explicit formulas for the nontrivial classical solutions of the corresponding adjoint homogeneous problem. Further, we give an exact integral representation of the generalized solutions of the cons

References

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    AIP Conference Proceedings, vol. 2172, issue 30016, pp. 1 - 7, 2019, United States, https://doi.org/10.1063/1.5133505

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