Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Classical Solution of a Problem with Integral Conditions of the Second Kind for the One-Dimensional Wave Equation

Classical Solution of a Problem with Integral Conditions of the Second Kind for the... for the one-dimensional wave equation given in a half-strip, we consider a boundary value problem with the Cauchy conditions and two nonlocal integral conditions. Each integral condition is a linear combination of a linear Fredholm integral operator along the lateral side of the half-strip applied to the solution and the values of the solution and of a given function on the corresponding base of the half-strip. Under the assumption of appropriate smoothness of the right-hand side of the equation and the initial data, we obtain a necessary and sufficient condition for the existence and uniqueness of a classical solution of this problem and propose a method for finding it in analytical form. A classical solution is understood as a function that is defined everywhere in the closure of the domain where the equation is considered and has all classical derivatives occurring in the equation and in the conditions of the problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Classical Solution of a Problem with Integral Conditions of the Second Kind for the One-Dimensional Wave Equation

Download PDF
10 pages

Loading next page...
 
/lp/springer-journals/classical-solution-of-a-problem-with-integral-conditions-of-the-second-hrK9vCT0S1

References (18)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266119030091
Publisher site
See Article on Publisher Site

Abstract

for the one-dimensional wave equation given in a half-strip, we consider a boundary value problem with the Cauchy conditions and two nonlocal integral conditions. Each integral condition is a linear combination of a linear Fredholm integral operator along the lateral side of the half-strip applied to the solution and the values of the solution and of a given function on the corresponding base of the half-strip. Under the assumption of appropriate smoothness of the right-hand side of the equation and the initial data, we obtain a necessary and sufficient condition for the existence and uniqueness of a classical solution of this problem and propose a method for finding it in analytical form. A classical solution is understood as a function that is defined everywhere in the closure of the domain where the equation is considered and has all classical derivatives occurring in the equation and in the conditions of the problem.

Journal

Differential Equations – Springer Journals

Published: Apr 24, 2019

There are no references for this article.