• Corpus ID: 119712222

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… 
1 Citations

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

  • M. Dontsova
  • Mathematics
    Izvestiya 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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