The nonlocal solvability conditions in original coordinates for a system with constant terms

DOI10.2989/16073606.2022.2108520zbMath1521.35085OpenAlexW4294252230MaRDI QIDQ6170149

M. V. Dontsova

Publication date: 15 August 2023

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2022.2108520

zbMATH Keywords

Cauchy problemglobal estimatesfirst order partial differential equationsmethod of an additional argument

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Systems of nonlinear first-order PDEs (35F50) Initial value problems for systems of nonlinear first-order PDEs (35F55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• On the existence of a smooth bounded solution for a system of two first-order nonlinear partial differential equations.
• Boundary-value problem with Saigo operators for mixed type equation with fractional derivative
• Solvability of the Cauchy problem for a quasilinear system in original coordinates
• Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier–Greenspan approach
• Nonlocal solvability conditions for Cauchy problem for a system of first order partial differential equations with special right-hand sides
• Solvability of Cauchy problem for a system of first order quasilinear equations with right-hand sides $f_1={a_2}u(t,x) + {b_2}(t)v(t,x),$ $f_2={g_2}v(t,x)$
• Global solutions to the shallow water system with a method of an additional argument
• On nonlinear partial differential equations with two independent variables
• On Hyperbolic Partial Differential Equations
• Hyperbolic Conservation Laws in Continuum Physics