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

Learn More →

ON THE SECOND BOUNDARY-VALUE PROBLEM FOR THE AIRY EQUATION

ON THE SECOND BOUNDARY-VALUE PROBLEM FOR THE AIRY EQUATION D E M O N S T R A T I O MATHEMATICAVol. X X I XNo 41996Elzbieta Majewska, Jan PopiolekON THE SECOND BOUNDARY-VALUE PROBLEMFOR THE AIRY EQUATION1. IntroductionConsider the equationDzxu{x,t)-(1)Dtu{x,t)= 0.In [3] there has been examined the equation Dtu = mD^u which is calledthe Airy equation and is a linear version of the Korteweg-de Vries (KdV)equation. It arises in the description of the slow variation of a wave frontin coordinates moving with the wave. It also describes the propagation ofoscillatory wave packets. In [5], [6] it is proved that equation Dtu = D^u isone of the canonical forms of third order partial differential equations andit is called the equation with characteristics multiple (see [4], p. 132).The first boundary value problem (or also called the Cattabriga problem)for Airy equation has been examined in [2], [4]; moreover, in [3] the Cauchyproblem for this equation has been considered. Papers [9], [10] were devotedto solve contact problems for the said equation.This paper concerns the second boundary-value problem for equation(1) in the domainD = {(jc, i) G K 2 : 0 < X < 1, 0 < t < T},T = const. > 0.First, we shall examine properties of some integrals related to http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON THE SECOND BOUNDARY-VALUE PROBLEM FOR THE AIRY EQUATION

Demonstratio Mathematica , Volume 29 (4): 22 – Oct 1, 1996

Loading next page...
 
/lp/de-gruyter/on-the-second-boundary-value-problem-for-the-airy-equation-EFLSiSToOT

References (8)

Publisher
de Gruyter
Copyright
© by Elzbieta Majewska
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1996-0402
Publisher site
See Article on Publisher Site

Abstract

D E M O N S T R A T I O MATHEMATICAVol. X X I XNo 41996Elzbieta Majewska, Jan PopiolekON THE SECOND BOUNDARY-VALUE PROBLEMFOR THE AIRY EQUATION1. IntroductionConsider the equationDzxu{x,t)-(1)Dtu{x,t)= 0.In [3] there has been examined the equation Dtu = mD^u which is calledthe Airy equation and is a linear version of the Korteweg-de Vries (KdV)equation. It arises in the description of the slow variation of a wave frontin coordinates moving with the wave. It also describes the propagation ofoscillatory wave packets. In [5], [6] it is proved that equation Dtu = D^u isone of the canonical forms of third order partial differential equations andit is called the equation with characteristics multiple (see [4], p. 132).The first boundary value problem (or also called the Cattabriga problem)for Airy equation has been examined in [2], [4]; moreover, in [3] the Cauchyproblem for this equation has been considered. Papers [9], [10] were devotedto solve contact problems for the said equation.This paper concerns the second boundary-value problem for equation(1) in the domainD = {(jc, i) G K 2 : 0 < X < 1, 0 < t < T},T = const. > 0.First, we shall examine properties of some integrals related to

Journal

Demonstratio Mathematicade Gruyter

Published: Oct 1, 1996

There are no references for this article.