## View abstract

### 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. document.getElementById('cloak92d2ab12c629e8d3752a287f25ac8a16').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy92d2ab12c629e8d3752a287f25ac8a16 = 'jmj&#105;m&#101;n&#101;' + '&#64;'; addy92d2ab12c629e8d3752a287f25ac8a16 = addy92d2ab12c629e8d3752a287f25ac8a16 + '&#117;n&#97;l' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;'; var addy_text92d2ab12c629e8d3752a287f25ac8a16 = 'jmj&#105;m&#101;n&#101;' + '&#64;' + '&#117;n&#97;l' + '&#46;' + '&#101;d&#117;' + '&#46;' + 'c&#111;';document.getElementById('cloak92d2ab12c629e8d3752a287f25ac8a16').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy92d2ab12c629e8d3752a287f25ac8a16 + '\'>'+addy_text92d2ab12c629e8d3752a287f25ac8a16+'<\/a>';

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).