<abstract xmlns="http://www.w3.org/1999/xhtml"> 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.</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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The mixed problem for quasilinear hyperbolic system with coefficients functionally dependent on the solution is studied. We assume that the coefficients are...

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

Published Online: Mar 31, 2018

Page range: 215 - 215

Received: Nov 04, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/auom-2017-0046

Keywords
Hyperbolic system, differential-functional equations, functional dependence on solution, method of characteristics, mixed problem

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 31, 2018

Page range: 215 - 215

Received: Nov 04, 2016

Accepted: Dec 21, 2016

DOI: https://doi.org/10.1515/auom-2017-0046

KeywordsHyperbolic system, differential-functional equations, functional dependence on solution, method of characteristics, mixed problem

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Hyperbolic system, differential-functional equations, functional dependence on solution, method of characteristics, mixed problem