Using Hodge theory for a surface, we obtain a new representation for solutions to the time harmonic Maxwell equations in both bounded and unbounded domains of R^3. This representation has no spurious resonances, does not suffer from low frequency breakdown, and reduces standard boundary value problems to Fredholm equations of second kind. There ...
Creator:
Epstein, Charles L. (University of Pennsylvania)
Created:
2013-10-28
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Saint-Venant system of shallow water equations and related models arewidely used in many scientific applications related to modeling of waterflows in rivers, lakes and coastal areas. The development of robust andaccurate numerical methods for the computation of the solutions to shallowwater models is an important and challenging problem.The Sain...
Creator:
Epshteyn, Yekaterina (The University of Utah)
Created:
2014-10-16
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
In the lectures, I will first introduce and review several chemotaxis models including the classical Patlak-Keller-Segel model. Chemotaxis is the phenomenon in which cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals (chemoattractants) in their environment. Chemotaxis is an imp...
Creator:
Epshteyn, Yekaterina (The University of Utah)
Created:
2013-07-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.