Organizers: Lorena Bociu (NC State University) and George Avalos (University of Nebraska-Lincoln)
We are pleased to announce the initiation of our IFIP TC 7.2. Virtual Seminar Series, which will run on a monthly basis. The purpose of this series is to promote the exchange of ideas, experiences and recent developments of researchers from all nations, during these difficult times when we cannot travel and interact in person. More information on IFIP TC 7 and its working groups can be found at https://ifip-tc7.impan.pl/ .[The seminar will run every month at 12pm EST USA. The seminar time is chosen so that we accommodate – as much as possible – people attending from all over the world. For your reference, here’s an interactive time zone map https://www.timeanddate.com/time/map/].
All are welcome to join us via Zoom. If interested, please email me for the Zoom link.
- June 1, at 12pm EST (noon) USA
Professor Sarka Necasova (Institute of Mathematics, Czech Academy of Sciences)
Title: A bi-fluid model for a mixture of two compressible non interacting fluids with general boundary data
Abstract: We deal with the global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The geometrical setting is general enough to comply with most current domains important for applications as, for example, (curved) pipes of picewise regular and axis-dependent cross sections. Moreover, we introduce dissipative turbulent solutions and prove an existence of such solutions for all adiabatic coefficients γ > 1, their compatibility with classical solutions, the relative energy inequality, and the weak strong uniqueness principle in this class. The class of dissipative turbulent solutions is so far the largest class of generalized solutions which still enjoys the weak strong uniqueness property. It is a joint work with S. Kracmar, B. J. Jin, Y. Kwon and A. Novotny.
- May 4, at 12pm EST (noon) USA – Talk was postponed to October 5, 2021.
Professor Fredi Troeltzsch (Technische Universität Berlin, Germany)
Title: Space-Time FEM for the Optimal Control of Reaction Diffusion Equations
Abstract: The numerical solution of forward-backward optimality systems, the necessary optimality conditions for parabolic optimal control problems, is still a challenge for spatial dimension d ≥ 2. We present and analyze a space-time finite element method on fully unstructured simplicial space-time meshes for solving such systems at once. Here, the time variable t is considered as just another spatial variable, say, the (d+1)th. For a linear state equation,
well-posedness of the system and associated discretization error estimates are shown by Babuska’s theorem. As application, we exemplarily consider the optimal control of the Schlogl model, a semilinear heat equation with non-
monotone third order polynomial nonlinearity, where traveling wave fronts occur as typical solutions. Numerical examples are presented that shed light on the control of traveling wave fronts, where space-time methods are particularly suitable. This is joint work with Ulrich Langer and Huidong Yang (RICAM Linz) and Olaf Steinbach (TU Graz).
- April 6, at 12pm EST (noon) USA
Professor Suncica Canic (University of California, Berkeley, USA)
Title: Mathematical Design of a Bioartificial Pancreas
Abstract: With the recent developments of new technologies in biomedical engineering and medicine, the need for new mathematical and numerical methods to aid these developments has never been greater. In particular, the design of an implantable bioartificial pancreas for the treatment of Type 1 diabetes hinges on the development of mathematical and computational techniques for solving nonlinear moving boundary problems. In this talk we present a complex, multi-scale model, and a recent well-posedness result in the area of fluid-poroelastic structure interaction, which have helped the design of a first implantable bioartificial pancreas without the need for immunosuppressant therapy. This is a joint work with bioengineer Shuvo Roy (UCSF), and mathematicians Yifan Wang (UCI), Lorena Bociu (NCSU), Boris Muha (University of Zagreb), and Justin Webster (University of Maryland, Baltimore County)
- March 2, at 12pm EST (noon) USA.
Professor Alberto Bressan (The Pennsylvania State University, USA)
Title: Traffic flow on a network of roads
Abstract: A mathematical description of traffic flow can be provided in terms of conservation laws, describing the density of cars along each road. Additional conditions are then used, to model flow at intersections. One can also look at daily traffic patterns as the result of the decisions of a large number of drivers, trying to minimize the time spent on the road and a penalty for late arrival. This leads to the problem of finding a globally optimal solution, which minimizes the sum of the costs to all drivers, or a Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time or his route to reach destination. The talk will review some of these models, discussing main results and current research directions.
- February 2, at 12pm EST (noon) USA.
Professor Christian Clason (University of Duisburg-Essen, Germany)
Title: Optimal control of non-smooth partial differential equations
Abstract: This talk is concerned with PDE-constrained optimization problems where the PDE constraint involves Lipschitz continuous but not classically differentiable terms. Correspondingly, the control-to-state mapping is not differentiable either, and classical approaches fail. In particular, there exists a zoo of optimality conditions of different strengths, roughly corresponding to different generalized derivatives of the control-to-state mapping. We derive such optimality conditions for model problems and discuss how they can be used for their numerical solution. This talk is based on joint work with Constantin Christof, Christian Meyer, Vu Huu Nhu, and Arnd Rösch.