Propiedades del soporte de soluciones de una clase de ecuaciones de evolución no lineales en dos dimensiones

Abstract

In this work we consider equations of the form ∂tu + P(D)u + u^{l}∂xu = 0, where P(D) is a two-dimensional differential operator, and l ∈ N. We prove that if u is a sufficiently smooth solution of the equation, such that suppu(0), suppu(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R0>0 such that suppu(t) ⊂ [-R_0,R_0]×[-R_0,R_0] for every t ∈ [0, T].