在這三年的研究計畫中, 我們將探討下列極富挑戰的的研究主題:對於一些重要及 附有動機的拋物型演化模型與具臨界非限性指數橢圓偏微分方程中, 奇異點集對此 類方程其解的基本性質, 如整體時間上之存在性, 唯一性, 爆破性等的影響之探討. ;In this three years researching project, we are interested in: how about the singularities affect the existence and structure of solutions for some motivated elliptic equations with Sobolev exponent and parabolic evolutions models. In the first year of this research project, we are interested in how the geometry of boundary singularities can affect the existence of positive solutions of elliptic equations. In the second year, we will focus on the more challenge and interesting researching topic that: how about the singularity behaviors of potential function $V$ and the critical power of the nonlinear term $f$ affect the global existence, uniqueness, blow-up and the fundamental properties of the solutions for the parabolic evolution pde. In the third year of this project, we will work on the time evolution equations with a singular potential on the boundary.
