Research 

• My primary research goals are directed towards understanding the effects of stochastic forcing on the solutions of nonlinear Cauchy and Dirichlet problems for PDEs, both analytically and numerically.

• My research involvements are also aimed towards understanding the theory of convergence of an adaptive finite element scheme for nonlinear stochastic parabolic problems which includes to develop an adaptive finite element method for nonlinear parabolic PDEs perturbed by multiplicative noise, and design a time-space adaptive algorithm to optimize the computation (of numerical solution).

• The theory of micromagnetism/ferromagnetism under random influences (stochastic Landau-Lifshitz-Gilbert equation) and the optimization of the switching dynamics, domain wall motion in a ferromagnetic nanowire, and optimal control problem for a coupled spin drift-diffusion Landu-Lifshitz-Gilbert system on a magnetic multilayer. 

• The well-posedness theory, related control problem and various qualitative properties for evolutionary nonlinear p-Laplace type stochastic PDEs driven by multiplicative Levy noise.