**Upcoming Events**

Wednesday, March 29, 2017 at 3:00 PM in 4201

Wen Shen, Penn State UniversityVanishing viscosity solutions for Riemann problems in polymer flooding

We visit several models of polymer flooding in reservoir simulation.

A special common feature shared by the models, i.e., the thermo-dynamics is decoupled from the hydro-dynamics, leads to a scalar conservation law with discontinuous flux. We discuss solution of Riemann problems as the vanishing viscosity limit. In particular, we show by counter examples that there exists infinitely many vanishing viscosity solution as one varies the ratio of the two viscosity parameters. However, adding two monotonicity conditions, all double limits will converge to the same function.

Wednesday, April 12, 2017 at 3:00 PM in SAS 4201

Harbir Antil, George Mason UniversityTBA

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Wednesday, April 19, 2017 at 3:00 PM in SAS 4201

Michele Palladino, Penn State UniversityGROWTH MODEL FOR TREE STEMS AND VINES

In this talk, we propose a model describing the growth of tree stems and vine, taking into account also the presence of external obstacles. The system evolution is described by an integral differential equation which becomes discontinuous when the stem hits the obstacle. The stem feels the obstacle reaction not just at the tip, but along the whole stem. This fact represents one of the main challenges to overcome, since it produces a cone of possible reactions which is not normal with respect to the obstacle. However, using the geometric structure of the problem and nonlinear analysis tools, we are able to prove existence and uniqueness of the solution under natural assumptions on the initial data.

Thursday, April 27, 2017 at 3:00 PM in SAS 4201

Nam Le, Department of Mathematics, Indiana UniversityTBA

TBA

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Seminar Organizer: Lorena Bociu, Khai Nguyen, and Michael Shearer