1) Asymptotic behavior of solutions to evolution problems (Decay of mass, Large time behavior of solutions).
2) Viscosity solutions for nonlinear problems (Comparison principle, Local existence and uniqueness of viscosity solutions, Ishii Lemma).
3) Nonlinear Elliptic, Parabolic and Hyperbolic PDEs (Local and Global existence, Blow-up, Blow-up rate, Strichartz estimtaes, Lp-Lq estimates, Energy space and estimate, Necessary conditions for local and global solutions, Fixed Point Theorem, Schauder's estimate, Interior's estimate, Fractional Sobolev Spaces).
4) Theory and Applications of Fractional Integrals and Derivatives (Fractional Laplacian, Riemann-Liouville integral and derivative operators).
5) Analytical solution (Homotopy Perturbation Method).
6) Seawater interface modeling.