# Global solutions to the shallow-water system

@article{Alexeenko2016GlobalST, title={Global solutions to the shallow-water system}, author={Sergey N. Alexeenko and Marina V. Dontsova and Dmitry E. Pelinovsky}, journal={arXiv: Analysis of PDEs}, year={2016} }

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class of initial data, we find a sufficient condition on the initial data that guarantees existence of a global classical solution continued from a local solution. The sufficient conditions can be easily satisfied for the fluid flow propagating in one direction with…

## One Citation

### Sufficient conditions of a nonlocal solvability for a system of two quasilinear equations of the first order with constant terms

- MathematicsIzvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
- 2020

We consider a Cauchy problem for a system of two quasilinear equations of the first order with constant terms. The study of the solvability of the Cauchy problem for a system of two quasilinear…

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