Applied and Computational Math Seminar: Analysis of the null controllability of space-time fractional diffusion equations

ANALYSIS OF THE NULL CONTROLLABILITY OF SPACE-TIME FRACTIONAL DIFFUSION 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.

Here0<α≤2,0<s≤1,Ω⊂RN isanopensetwithboundary∂Ω,(−∆)s thefractional 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 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