On the support of solutions to the generalized KdV equation

Luis Vega; Carlos E. Kenig; Gustavo Ponce

doi:10.1016/s0294-1449(01)00073-7

JournalsaihpcVol. 19, No. 2pp. 191–208

On the support of solutions to the generalized KdV equation

Luis Vega
Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao, Spain
Carlos E. Kenig
Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
Gustavo Ponce
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

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Abstract

It is shown that if u is a solution of the initial value problem for the generalized Korteweg–de Vries equation such that there exists $b \in R$ with $supp u (., t_{j}) \subseteq (b, \infty)$ (or (−∞,b)), for j=1,2 (t1≠t2), then u≡0.

Résumé

On montre que si u est une solution du problème de Cauchy pour l'équation généralise de Korteweg–de Vries et $b \in R$ tel que $supp u (., t_{j}) \subseteq (b, \infty)$ (ou (−∞,b)), pour j=1,2 (t1≠t2), alors u est nulle.

Cite this article

Luis Vega, Carlos E. Kenig, Gustavo Ponce, On the support of solutions to the generalized KdV equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002), no. 2, pp. 191–208

DOI 10.1016/S0294-1449(01)00073-7