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Dr. Peter Polacik from the University of Minnesota will join us at UTSA on Friday April 22 to discuss:
Propagating Terraces in the Dynamics of Front-like Solutions of Parabolic Equations
We consider semilinear parabolic equations on the real line. By a front-like solution we mean a solution u(x, t) which has limits as x → ±∞ equal to constant steady states ±γ. In many well studied cases, the behavior of such solutions is governed by a traveling front connecting the steady states γ and −γ. However, in general, such a traveling front does not exist. We explain in the lecture how a more general concept, a propagating terrace, or a stacked system of traveling fronts, can used to describe the large time-behavior of front-like solutions.