Research Interests
My research since my PhD has had two primary foci. (1) Partial Differential equations, specifically,Improperly posed problems, systems of reaction-diffusion equations, nonlinear wave equations and the longtime behavior of their local (in time) solutions. (2) Mathematical biology, specifically the study of tumor angiogenesis and genetic switches such as p53. Applied discrete dynamical systems, specifically the analysis of oligonucleotide enrichment processes such as SELEX.
I have also worked on various other problems from time to time such as intermittent current effects in free electrophoresis, the movement of surfactant on the surface of forming droplets and inequalities between Dirichlet and Neuman eigenvalues of the Laplacian.
You will find a fairly complete list of my publications at MathSciNet (American Mathematical Society).
Graduate Student and Post Doctoral supervision.
I have directed Master theses and nine PhD dissertations . I have also supervised post doctorate fellow, Joanna Renclawowicz (NATO) and one masters fellow, Valentina Burmistrova, MS (Fulbright).
Click on Partial Differential Equations for more information on Partial Differential Equations at Iowa State University.