Applied and Computational Math Seminar: Fractional Powers of Parabolic Operators and Master Equation

Fractional Powers of Parabolic Operators and Master Equation

Animesh Biswas Iowa State University

Abstract: In this talk we will define the fractional power of parabolic operator. Using Fourier Transform, we get a definition of the fractional power of the heat operator, i.e (∂t − ∆)s for 0 < s < 1. Then the following integral representation of Gamma function,

􏰂∞􏰀 0t

Γ(−s)=
and its analytic continuation in the complex Right Half Plane with Cauchy

Integral formula gives a Semi-group formulation of the fractional power of

ss
(∂t − ∆) . This also gives us a point-wise formula for (∂t − ∆) u. Then we

s
will give the Harnack inequality for the operator (∂t − ∆) . Finally we will

talk about the fractional power of the operator (∂t + L), where L is an elliptic operator in divergence form and the corresponding Harnack inequality.

Time: Friday, April 12, 2019, 1:30-2:30pm Place: Exploratory Hall, Room 4106

Department of Mathematical Sciences George Mason University
4400 University Drive, MS 3F2 Fairfax, VA 22030-4444 http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491