Summary
We prove the existence and uniqueness of weak solutions of the mixed problem for a class of systems of nonlinear Klein-Gordon equations. Uniqueness is proved when the spatial dimension is either n=1, 2or 3.
Article PDF
Similar content being viewed by others
References
J.Ferreira - G.Perla Menzala,Decay of solutions of a system of nonlinear Klein-Gordon equations (to appear).
K.Jörgens,Nonlinear wave equations, University of Colorado, Department of Mathematics, 1970.
J. L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
J. L. Lions -E. Magenes,Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968.
J. L. Lions -W. A. Strauss,Some non linear evolutions equations, Bull. Soc. Math. de France,95 (1965), pp. 43–96.
V. G. Makhankov,Dynamics of classical solutions in integrable systems, Physics Reports (Section C of Physics Letters),35 (1) (1978), pp. 1–128.
L. A.Medeiros - G.Perla Menzala,On a mixed problem for a class of nonlinear Klein-Gordon equations (to appear).
I. Segal,Nonlinear partial differential equations in Quantum Field Theory, Proc. Symp. Appl. Math. A.M.S.,17 (1965), pp. 210–226.
M. I.Visik - O. A.Ladyzhenskata,On boundary value problems for partial differential equations and certain class of operator equations, A.M.S. Translations Series 2, vol. 10, 1958.
Author information
Authors and Affiliations
Additional information
Partially supported by CNPq-Brasil.
Rights and permissions
About this article
Cite this article
Medeiros, L.A., Miranda, M.M. Weak solutions for a system of nonlinear Klein-Gordon equations. Annali di Matematica pura ed applicata 146, 173–183 (1986). https://doi.org/10.1007/BF01762364
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01762364