Focus on existence, stability and long time behavior studies, as well as numerical schemes.
Fokker-Planck type integrodifferential models for density of blood vessel tips
– Mathematical foundation for these models by proving the existence, uniqueness, and stability of solutions in various geometries, including the whole space and specialized annular domains. This involves constructing Green functions, establishing sharp estimates for velocity integrals and employing PL Lions compensated compactness.
narwa16 amm17
– Positivity preserving, stable and converging numerical schemes: From low first order upwind approaches to high order WENO-SSH schemes.
jcp18 ijnsns21
Kinetic equations for semiconductors and plasmas
– Vlasov-Poisson-Boltzmann system for the motion of charged particles in semiconductors: Long-time asymptotics of these equations, determining how solutions behave as time approaches infinity, by means of employing PL Lions compensated compactness methods.
mmmas01
– Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term: First numerical solutions for a kinetic theory description of self-sustained current oscillations in n-doped semiconductor superlattices. Solved via a deterministic Weighted Particle Method.
jcp09
– Vlasov-Poisson-Fokker-Planck system for plasmas: Long-time asymptotics of these equations, by constructing fundamental solutions for linearized operators with variable coefficients.
mmas98
