A MIXED PROBLEM FOR A NONHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEM OF EQUATIONS

1984 ◽  
Vol 48 (1) ◽  
pp. 201-210
Author(s):  
V Yu Lyapidevskiĭ
Keyword(s):  
Mixed Problem ◽  
Hyperbolic System ◽  
System Of Equations ◽  
Quasilinear Hyperbolic System ◽  
Hyperbolic System Of Equations

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

2017 ◽  
Vol 25 (3) ◽  
pp. 215
Author(s):  
Małgorzata Zdanowicz ◽  
Zbigniew Peradzyński
Keyword(s):  
Banach Space ◽  
Initial Data ◽  
Mixed Problem ◽  
Hyperbolic System ◽  
Quasilinear Hyperbolic System ◽  
Nonlinear Operators ◽  
Uniqueness And Existence ◽  
Class C ◽  
Additional Assumptions

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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