Shibin Dai

Dr. Dai is an Associate Professor and the Graduate Program Director of the Department of Mathematics, College of Arts & Sciences. He is a mathematician that has a genuine interest in a wide range of real world problems. He studies mathematical problems that arise in physical, biological, and materials sciences. His research has been supported by NSF grants. 

Representative Publications

  1. Minimizers for the Cahn-Hilliard energy under strong anchoring conditions, S. Dai, B. Li, T. Luong. SIAM J. Appl. Math 80: 2299-2317 2020. 
  2. Rigorous derivation of a mean field model for the Ostwald ripening of thin films, S. Dai, Communications in Mathematical Sciences 18: 293-320, 2020.
  3. Convergence of phase-field free energy and boundary force for molecular solvation, S. Dai, B. Li, J. Lu. Archive for Rational Mechanics and Analysis 227: 105-147, 2018.
  4. Weak solutions for the Cahn-Hilliard equation with degenerate mobility, S. Dai, Q. Du. Archive for Rational Mechanics and Analysis 219: 1161—1184, 2016.
  5. Motion of interfaces governed by the Cahn-Hilliard equation with highly disparate diffusion mobility, S. Dai, Q. Du. SIAM J. Appl. Math 72: 1818-1841, 2012.

Research Interests

Dr. Dai is research interest lie in nonlinear partial differential equations, applied analysis, and numerical analysis, with applications in physical, biological, and materials science. Specific areas include: network formation in amphiphilic mixtures with applications to lipid bilayer evolution and morphology in polymer electrolyte materials; phase-field variational models for molecular solvation; domain coarsening and self-similarity in materials science, phase transitions and thin films; free boundary problems.