Existence and Uniqueness in the Linearised One and Two-dimensional Problem of Partial Differential Equations With Variational Method

Abstract

The classical solution and the strong solution of a partial differential equation problem are continuously differentiable solutions. This solution has a derivative for a continuous infinity level. However, not all problems of partial differential equations can be easily obtained by strong solutions. Even the existence of a solution requires in-depth investigation. The variational formulation method can qualitatively analyze a single solution to a partial differential equation problem. This study provides an alternative method in analyzing the problem model of partial differential equations analytically. In this research, we will examine the partial differential equation modelling built from fluid dynamics modelling.