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  JP Journal of Fixed Point Theory and Applications  
 ISSN: 0973-4228
 
 
 

     JP Journal of Fixed Point Theory and Applications
    Volume 3, Issue 1, Pages 49 - 61 (April 2008)


A CONTRACTED PROCEDURE FOR THE UNIQUE SOLVABILITY OF A SEMI-LINEAR WAVE EQUATION ASSOCIATED WITH A LINEAR INTEGRAL EQUATION AT THE BOUNDARY

Le V. Ut (Vietnam)

Received December 23, 2007

References:



[1] N. T. An and N. D. Trieu, Shock between absolutely solid body and elastic bar with the elastic viscous frictional resistance at the side, Vietnam J. Mech. NCSR., Tom XIII(2) (1991), 1-7.

[2] H. Brezis, Analyse Fonctionnelle: Théorie et Applications, Masson, Paris, 1983.

[3] Lawrence C. Evans, Partial differential equations, Grad. Stud. Math., Vol. 19, Amer. Math. Soc., Providence, RI, 1998.

[4] J. L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non-linéaires, Dunod-Gauthier-Villars, Paris, 1969.

[5] N. T. Long and A. P. N. Dinh, A semilinear wave equation associated with a linear differential equation with Cauchy data, Nonlinear Anal. 24 (1995), 1261-1279.

[6] N. T. Long, Le V. Ut and N. T. T. Truc, A shock of a rigid body and a linear viscoelastic bar, Hcm Ped. Univ. J. Natur. Sci. 4(38) (2004), 27-40.

[7] N. T. Long, Le V. Ut and N. T. T. Truc, A shock of a rigid body and a linear viscoelastic bar: Global existence and stability of the solutions, Hcm Ped. Univ. J. Natur. Sci. 6(40) (2005), 26-39.

[8] N. T. Long, Le V. Ut and N. T. T. Truc, A shock problem involving a linear viscoelastic bar, Nonlinear Anal. 63 (2005), 198-224.

[9] N. T. Long, Le V. Ut and L. X. Truong, Mathematical model for a shock problem involving a nonlinear viscoelastic bar (2006), preprint.

[10] M. L. Santos, Asymptotic expansion of solutions to wave equations with a memory condition at the boundary, Electron. J. Differential Equations 73 (2001), 1-11.

[11] M. T. Sengul, An effective method for the existence of the global attractor of a nonlinear wave equation, Appl. Math. E-Notes 7 (2007), 179-185.

[12] G. Teschl, Nonlinear functional analysis, Lecture Notes in Math., Vienna Univ., Austria, 2001.

[13] Le V. Ut, The well-posedness of a semilinear wave equation associated with a linear integral equation at the boundary, Mem. Differential Equations Math. Phys. (2007) to appear.

[14] Le V. Ut and Eduardo Pascali, A contracted procedure for the unique solvability of a simi-linear wave equation associated with a full nonlinear damping source and a linear integral equation at the boundary (in preparation).

[15] E. Zeidler, Nonlinear Functional Analysis and its Applications, Vol. II, Springer-Verlag, Leipzig, 1989.

Keywords and phrases: contracted procedure, semi-linear wave equation, linear integral equation, unique solvability.

 


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