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The order completion method for systems of nonlinear PDEs: solutions of initial value problems. (English) Zbl 1308.35011

Summary: We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each such solution may be represented in a canonical way through its generalized partial derivatives as nearly finite normal lower semicontinuous function.

MSC:

35A25 Other special methods applied to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35D30 Weak solutions to PDEs
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