scholarly journals THE DARBOUX AND KOSHI PROBLEM FOR LINEAR HYPERBOLIC EQUATIONS WITH CONSTANT COEFFICIENTS

2021 ◽  
Vol 6 (12(81)) ◽  
pp. 15-18
Author(s):  
Z. Usipbek ◽  
D. Aubakir ◽  
D. Bexapar ◽  
Zh. Ashirkhan ◽  
A. Shekerbek
Keyword(s):  
Hyperbolic Equations ◽  
Explicit Representation ◽  
Darboux Problem ◽  
Constant Coefficients ◽  
Linear Hyperbolic Equations

Many phenomena of mechanics, physics, and biology are reduced to the study of hyperbolic equations. In order to describe these phenomena completely, the Darboux problem is posed for hyperbolic equations, and for further studies, an explicit representation of the problem under consideration is necessary. In this article discusses, we study the Darboux and Koshi problems for linear hyperbolic equations with constant coefficients.

Fast high order ADER schemes for linear hyperbolic equations

2004 ◽  
Vol 197 (2) ◽  
pp. 532-539 ◽  
Author(s):  
Thomas Schwartzkopff ◽  
Michael Dumbser ◽  
Claus-Dieter Munz
Keyword(s):  
Hyperbolic Equations ◽  
High Order ◽  
Linear Hyperbolic Equations

scholarly journals On the exponential growth of solutions to non-linear hyperbolic equations

1989 ◽  
Vol 12 (3) ◽  
pp. 539-545 ◽  
Author(s):  
H. Chi ◽  
H. Poorkarimi ◽  
J. Wiener ◽  
S. M. Shah
Keyword(s):  
Exponential Growth ◽  
Hyperbolic Equations ◽  
Uniqueness Theorems ◽  
Continuous Solutions ◽  
Unbounded Region ◽  
Non Linear ◽  
Growth Of Solutions ◽  
Linear Hyperbolic Equations

Existence-uniqueness theorems are proved for continuous solutions of some classes of non-linear hyperbolic equations in bounded and unbounded regions. In case of unbounded region, certain conditions ensure that the solution cannot grow to infinity faster than exponentially.

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