scholarly journals On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term.

2004 ◽  
Vol 17 (1) ◽  
Author(s):  
Filipa Caetano
Keyword(s):  
Cauchy Problem ◽  
Weak Solutions ◽  
Source Term ◽  
Hyperbolic Equations ◽  
Quasilinear Hyperbolic Equations ◽  
Existence Of Weak Solutions ◽  
The Cauchy Problem

scholarly journals Cauchy problem for hyperbolic equations of third order with variable exponent of nonlinearity

2020 ◽  
Vol 12 (2) ◽  
pp. 419-433
Author(s):  
O.M. Buhrii ◽  
O.T. Kholyavka ◽  
P.Ya. Pukach ◽  
M.I. Vovk
Keyword(s):  
Cauchy Problem ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Lebesgue Spaces ◽  
Third Order ◽  
The Third ◽  
The Cauchy Problem

We investigate weak solutions of the Cauchy problem for the third order hyperbolic equations with variable exponent of the nonlinearity. The problem is considered in some classes of functions namely in Lebesgue spaces with variable exponents. The sufficient conditions of the existence and uniqueness of the weak solutions to given problem are found.

On the existence of weak solutions for a nonlinear time dependent Dirac equation

1989 ◽  
Vol 113 (1-2) ◽  
pp. 149-158 ◽  
Author(s):  
João-Paulo Dias ◽  
Mário Figueira
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Dirac Equation ◽  
Characteristic Function ◽  
Weak Solutions ◽  
Time Dependent ◽  
Existence Of Weak Solutions ◽  
Nonlinear Dirac Equation ◽  
The Cauchy Problem ◽  
Image Position

SynopsisIn this paper we prove the existence of a weak solution of the Cauchy problem for the nonlinear Dirac equation in ℝ × ℝwhere X(r) is the characteristic function of a compact interval of ]0, + ∞[

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