Dear Colleagues,

We continue our Colloquium in the Math Department.

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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.