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My research focuses on partial differential equations and applied analysis, with particular emphasis on diffuse-domain methods and nonlinear phase-field models. I develop rigorous analytical tools to study singular limits, convergence rates, and the existence of physically admissible weak solutions. 

My recent work examines how diffuse-interface approximations and vanishing diffusion coefficients affect convergence to PDEs posed on complex domains, building on my earlier research on degenerate phase-field equations arising in phase separation, amphiphilic self-assembly, and crystalline materials.