Browse > Article

HYPERBOLIC EQUATION FOR FOURTH ORDER WITH MULTIPLE CHARACTERISTICS  

Bougoffa, Lazhar (Department of Mathematics, Faculty of Science, Al-Imam University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.3_4, 2010 , pp. 837-844 More about this Journal
Abstract
In this paper, a class of initial value problem of hyperbolic equations for fourth order with multiple characteristics is considered and can be solved analytically by variable transforms. Also, similar to Goursat's problem we present a direct integration technique for finding a new solutions of an inhomogeneous hyperbolic equation of fourth order such that the attached conditions are given on its multiple characteristics.
Keywords
Hyperbolic equation for fourth order; multiple characteristics; Goursat's problem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. S. Agranovich, Boundary value problems for systems with a parameter, Matem. Sbornik, 84(1971), No. 1, 27-65(Russian; Engl.transl. in Math. USSR Sbornik 13(1971), 27-65.
2 R. Beals, Hyperbolic equations and systems with multiple characteristics, Arch. Rational Mech. Anal. 48(1972), 123-152..
3 S. Agmon, Probleme mixte pour les equations hyperboliques d'ordre superieur, Colloq. Intern. CNRS, Paris (1962), 1-6.
4 Y. Ohya and S. Tarama, Le probleme de Cauchy a caracteristiques multiples coefficients holderiens en t, Proc. Taniguchi International Symposium on Hyperbolic Equations and Related Topics (1984), 273-306.
5 H. O. Kreiss, Initial boundary value problems for hyperbolic systems, Communs Pure and Appl. Math. 23(1970), 277-298.   DOI
6 L. Bougoffa, The Cauchy problem for nonlinear Hyperbolic equations of higher order using Modified decomposition method, J. Math. Cont. Sc. and Appl, 1(2007), 11-19.
7 M. D. Bronstein, The Cauchy problem for hyperbolic operators with characteristics of variable multiplicity, Trudy Moskov. Mat. Obsc. 41(1980), 87-103.
8 F. Colombini and T. Kinoshita, On the weakly hyperbolic equation of 4th order, Hokkaido Math. J. 31(2002), 39-60.
9 A. Lax, On Cauchy's problem for partial differential equations with multiple characteristics, Comm. Pure Appl. Math. 9(1956), 135-169.   DOI
10 B. Midodashvili, A nonlocal problem for fourth order hyperbolic equations with multiple characteristics, Electron. J. Diff. Eqns. 85(2002), 1-7.