Cauchy problem for quasilinear hyperbolic systems with coeffcients functionally dependent on solutions (Archives of Mechanics - Test, 2007)
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.