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On the well-posedness of some generalized characteristic Cauchy problems. (English) Zbl 1398.35285
Summary: By means of convenient regularization for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we show existence and uniqueness of the solution.
MSC:
35R25 Ill-posed problems for PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35A25 Other special methods applied to PDEs
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
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