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 aboutthe singularities affect the existence and structure of solutions forsome motivated elliptic equations with Sobolev exponent and parabolicevolutions models. In the first year of this research project, we areinterested in how the geometry of boundary singularities can affect theexistence of positive solutions of elliptic equations.In the second year, we will focus on the more challenge and interestingresearching topic that: how about the singularity behaviors of potentialfunction $V$ and the critical power of the nonlinear term $f$ affect theglobal existence, uniqueness, blow-up and the fundamental properties ofthe solutions for the parabolic evolution pde. In the third year of thisproject, we will work on the time evolution equations with a singularpotential on the boundary.
