Research
My research is in partial differential equations, with a particular interest in problems related to conservation laws. I am currently interested in the stability of traveling waves for viscous conservation laws and in the interaction between shock waves and boundaries.
Research Interests
- Partial Differential Equations
- Conservation Laws
- Viscous Shock Waves and Boundary Layers
- Partial Differential Equations in Fluid Dynamics
- Singular Perturbation Problems
Current Research
I am currently studying the asymptotic stability of traveling waves for viscous conservation laws on a half-line. In particular, I am interested in the behavior of viscous shock waves propagating toward a boundary and in the transition to a different asymptotic state through their interaction with the boundary.
Recently, I have been studying the viscous Burgers equation as a model problem, focusing on the transition of an incoming viscous shock wave to a boundary layer. I am also interested in extending this analysis to more general conservation laws and fluid equations.