Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 39 No. 1 (2021): Revista integración, temas de matemáticas
Research and Innovation Articles

Properties of the Support of Solutions of a Class of 2-Dimensional Nonlinear Evolution Equations.

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  • Eddye Bustamante,
  • José Jiménez Urrea
Eddye Bustamante
National university of Colombia
José Jiménez Urrea
National university of Colombia.
DOI: https://doi.org/10.18273/revint.v39n1-2021003

Published 2021-05-19

Keywords

  • Nonlinear evolution equations,
  • weighted Sobolev spaces,
  • Carleman estimates

How to Cite

Bustamante, E., & Jiménez Urrea, J. (2021). Properties of the Support of Solutions of a Class of 2-Dimensional Nonlinear Evolution Equations. Revista Integración, Temas De matemáticas, 39(1), 41–50. https://doi.org/10.18273/revint.v39n1-2021003

Copyright (c) 2021 Revista Integración, temas de matemáticas

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In this work we consider equations of the form

∂tu + P(D)u + u^{t}∂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 supp u(0), supp u(T) ⊂ [−B, B] × [−B, B] for some B > 0, then there exists R_0 > 0 such that supp u(t) ⊂ [-R_0,R_0]×[-R_0,R_0] for every t ∈ [0, T].

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