Wednesday, March 29, 2017 at 3:00 PM in 4201
Wen Shen, Penn State University
Vanishing 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 University
Wednesday, April 19, 2017 at 3:00 PM in SAS 4201
Michele Palladino, Penn State University
GROWTH 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 University
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