Applied and Computational Math Seminar: Controllability of space-time fractional diffusive and super-diffusive equations

CONTROLLABILITY OF SPACE-TIME FRACTIONAL DIFFUSIVE AND SUPER-DIFFUSIVE EQUATIONS

MAHAMADI WARMA

Abstract: We consider the following class of fractional partial differential equations of evolution in which two parameters are used to sharpen the models.

Dαt u(t,x)+(−∆)su(t,x)=f(t,u) on Ω×(0,T), + Intial conditions,

+ Boundary conditions.

HereT >0isafixedtime,0<α≤2,0<s≤1,Ω⊂RN isanopensetwithboundary∂Ω, (−∆)s is the fractional Laplace operator and Dαt denotes a time fractional derivative. After clarifying which initial and boundary conditions make the system well posed, we show what is so far known about the null controllability or/and the approximate controllability of the above system. We conclude by given several open problems. The talk will be delivered for a wide audience avoiding unnecessary technicalities.

M. Warma, University of Puerto Rico (Rio Piedras Campus), College of Natural Sciences, Department of Mathematics, PO Box 70377 San Juan PR 00936-8377 (USA)

E-mail address: mahamadi.warma1@upr.edu