本篇論文主要敘述一階偏微分方程的黏滯解其定義與性質。從最佳控制的觀點提出值函數 v，進而引導出 所滿足的Hamilton -Jacobi-Bellman方程，接著證明v為此方程的黏滯解。此外，加以証明黏滯解的唯一性、比較性與穩定性質。 The study of this thesis is to discuss the definition and property of the viscosity solution of first-order partial differential equations. To claim the value function in viscosity sense and guides the Hamilton -Jacobi-Bellman equation which is satisfied with . Then we prove that is the viscosity solution of this equation. Moreover, we also prove the uniqueness, comparison and stability of viscosity solutions.
