Dear Colleagues,

We continue our Colloquium in the Math Department.

*************************

Speaker: Jianlong Han*, Department of Mathematics, Michigan State University

Time/Place: Tuesday, March 15, 3:00 pm, EMCS 422.

Title: Nonlocal evolution equations

Abstract:
An interesting phenomenon is observed when one takes a molten binary
alloy and quenches it, i.e., rapidly lowers the temperature so that it
becomes solid. Immediately after the quench one observes that the
sample becomes inhomogeneous very quickly,decomposing into a very
fine-grained structure  - two concentration phases, one rich in one
component and one rich in the other component. As time passes, the
fine-grained structure becomes more coarse with large particles growing
and smaller particles tending to dissolve. The sudden appearance of a
fine grained structure is called spinodal decomposition. The coarsening
process is called Ostwald Ripening.

The first half of the talk will describe some detailed mathematical
models (nonlocal Cahn-Hilliard equations and nonlocal phase field
systems)  to predict spinodal decomposition and Ostwald ripening. Then I
will give results about the existence, uniqueness and continuous
dependence on initial data of the solution to the equation and system.
Also I will give a nonlinear version of the  Poincare inequality which
is used to show the existence of an absorbing set in each constant mass
affine space. Finally, I will discuss the numerical simulation for the
nonlocal Cahn-Hilliard equation.

* Jianlong Han is a candidate for a position at our Department.

--
John V. Matthews, III      \ http://www.utc.edu/Faculty/Matt-Matthews
Department of Mathematics   \ [log in to unmask]
Univ. of Tenn. at Chattanooga\ 423.425.4719       Hint: Use GNU/Linux