Broad area of my research is partial differential equations, more precisely the evolution equations. This includes dispersive PDEs and parabolic PDEs. I am interested in studying well-posedness, ill-posedness, stability, asymptotic behavior of these types of nonlinear PDEs with data in various spaces.
The equations I have worked on includes:
Dispersive PDEs: Schrodinger equation, KdV equation, mKdV equation, Hartree equation, Hartree-Fock equation, wave equation, Benjamin-Bona-Mahony equation
Parabolic & Elliptic equations: Heat equations, p-Laplace equation.
For my publications click here.