The purpose of the project is to study several types of nonlinear partial differential equations that arise in material science, solid mechanics, and cell biology. In particular, the goals of project are to study the relation between a variety of plate theories and three-dimensional elasticity theory by deriving the asymptotic limit of three-dimensional nonlinear elasticity, to justify the limit of a singularly perturbed functional as an Aviles-Giga functional, to investigate the evolution of interfaces in multi-phase polymer crystals growth by addressing the stability of moving fronts, and to deepen understanding of the homogenization limit of parabolic equations and of systems of elliptic equations in cell biology and polymer sciences.
The investigator studies nonlinear pertial differential equations that describe important behaviors of systems in polymers, materials, and cell biology. Clear understanding of the stability of moving interfaces helps control the interface between the melt and crystal to ensure high quality of polymer production. Theoretical guided computation of the Young modulus in polymer nanocomposites is important to measure the strength of micro-packaging material for computer chips. Identifying the corrected diffusion process for protein IP3 from cell membrane to highly convoluted endoplastic reticulum can save huge amounts of money and time in fundamental scientific research in cell biology.
