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Session S22 - Deterministic and probabilistic aspects of nonlinear evolution equations

Friday, July 16, 18:20 ~ 18:50 UTC-3

Properties of the Support of Solutions of a Class of Nonlinear Evolution Equations

José Manuel Jiménez

Universidad Nacional de Colombia- Sede Medellín, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this work we consider equations of the form $$\partial_t u+P(\partial_x) u+G(u,\partial_xu,\dots,\partial_x^l u)=0,$$ where $P$ is any polynomial without constant term, and $G$ is any polynomial without constant or linear terms. We prove that if $u$ is a sufficiently smooth solution of the equation, such that $\supp u(0),\supp u(T)\subset (-\infty,B]$ for some $B>0$, then there exists $R_0>0$ such that $\supp u(t)\subset (-\infty,R_0]$ for every $t\in[0,T]$. Then, as an example of the application of this result, we employ it to show unique continuation properties for some nonlinear dispersive models$$

Joint work with Eddye Bustamante (Universidad Nacional de Colombia-Sede Medellín).

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