Cauchy problem for quasilinear hyperbolic systems with coeffcients functionally dependent on solutions

doi:10.24423/aom.238

Vol 59, No 2 (2007)

Cauchy problem for quasilinear hyperbolic systems with coeffcients functionally dependent on solutions

M. Zdanowicz, Z. PeradzyÅ„ski

Arch. Mech. 59 (2), 173-197, 2007

Keywords: functional dependence on solutions; characteristic curves; Cauchy problem; hyperbolic system

Abstract

The Cauchy problem for a quasilinear hyperbolic systems with coeffcients functionally dependent on the solutions is studied. We assume that the coeffcients are continuous nonlinear operators in the Banach space C¹(â„) satisfying some additional assumptions. Under these assumptions we prove the uniqueness and existence of local in time C¹ solutions, provided that the initial data are also of class C¹.

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