Discontinuous solutions of quasilinear equations of the first order

1964 ◽  
pp. 1-6
Author(s):  
A. N. Tihonov ◽  
A. A. Samarskiĭ
Keyword(s):  
Quasilinear Equations ◽  
Discontinuous Solutions ◽  
First Order

scholarly journals The nonlocal solvability conditions for a system of two quasilinear equations of the first order with absolute terms

2019 ◽  
Vol 21 (3) ◽  
pp. 317-328
Author(s):  
Marina V. Dontsova
Keyword(s):  
Cauchy Problem ◽  
Finite Number ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Local Solution ◽  
Quasilinear Equations ◽  
Solvability Conditions ◽  
First Order ◽  
The Cauchy Problem ◽  
Global Estimates

The Cauchy problem for a system of two first-order quasilinear equations with absolute terms is considered. The study of this problem’s solvability in original coordinates is based on the method of an additional argument. The existence of the local solution of the problem with smoothness which is not lower than the smoothness of the initial conditions, is proved. Sufficient conditions of existence are determined for the nonlocal solution that is continued by a finite number of steps from the local solution. The proof of the nonlocal resolvability of the Cauchy problem relies on original global estimates.

scholarly journals First order quasilinear equations with boundary conditions

1979 ◽  
Vol 4 (9) ◽  
pp. 1017-1034 ◽  
Author(s):  
C. Bardos ◽  
A. Y. Leroux ◽  
J. C. Nedelec
Keyword(s):  
Boundary Conditions ◽  
Quasilinear Equations ◽  
First Order
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