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Cauchy problem for a linear hyperbolic equation of the second order

    V. I. Korzyuk Affiliation
    ; E.S. Cheb Affiliation

Abstract

The definition of hyperbolic equation by a prescribed vector field is introduced for linear differential equation of the second order. The Cauchy problem with prescribed boundary conditions is considered for such equations. The theorems of existence and uniqueness of a strong solution to the given problem are proved by the method of energy inequalities and mollifiers with variable step. 


First Published Online: 14 Oct 2010

Keyword : hyperbolic equation, Cauchy problem, strong solution, energy inequality, mollifiers

How to Cite
Korzyuk, V. I., & Cheb, E. (2006). Cauchy problem for a linear hyperbolic equation of the second order. Mathematical Modelling and Analysis, 11(3), 275-294. https://doi.org/10.3846/13926292.2006.9637318
Published in Issue
Sep 30, 2006
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This work is licensed under a Creative Commons Attribution 4.0 International License.