Mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on solution

Zdanowicz, Małgorzata; Peradzyński, Zbigniew

doi:10.1515/auom-2017-0046

Abstract

The mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on the solution is studied. We assume that the coefficients are continuous nonlinear operators in the Banach space C¹(ℝ) satisfying some additional assumptions. Under these assumptions we prove the uniqueness and existence of local in time C¹ solution, provided that the initial data are also of class C¹.

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Mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on solution

Abstract

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