Abstract

BUSTAMANTE, Eddye  and  JIMENEZ URREA, José. Properties of the Support of Solutions of a Class of 2-Dimensional Nonlinear Evolution Equations. Integración - UIS [online]. 2021, vol.39, n.1, pp.41-50.  Epub Feb 28, 2021. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n1-2021003.

In this work we consider equations of the form

where P(D) is a two-dimensional differential operator, and l ∈. We prove that if u is a sufficiently smooth solution of the equation, such that supp u(0),supp u(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R0 > 0 such that supp u(t) ⊂ [−R0, R0]×[−R0, R0] for every t ∈ [0, T].

Keywords : Nonlinear evolution equations; weighted Sobolev spaces; Carleman estimates; MSC2010: 35Q53; 37L50; 47J35.

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