Évènement

Date(s) : 13/03/2018   iCal
11h00 - 12h00

This work is concerned with the asymptotic behavior of bounded solutions of the Cauchy problem
$$
$$u_t=u_{xx} +f(t,u), qquad xin mathbb{R},,t>0,$$
$$u(x,0)= u_0 $$

where $u_0$ is a nonnegative bounded function with compact support and $f$ is periodic in $t$ and satisfies $f(cdot,0)=0$. We first prove that the $omega$-limit set of any bounded solution either consists of a single time-periodic solution or it consists of time-periodic solutions as well as heteroclinic solutions connecting them. Furthermore, under a minor nondegenerate assumption on time-periodic solutions of the corresponding ODE, the convergence to a time-periodic solution is proved. Lastly, we apply these results to equations with bistable nonlinearity and combustion nonlinearity, and specify more precisely which time-periodic solutions can possibly be selected as the limit.
This is a joint work with Hiroshi Matano.

http://www.mims.meiji.ac.jp/team/index-e.html

Catégories

• Séminaire