Free Access

Chapter 1: Introduction

https://doi.org/10.1142/9789813226449_0001Cited by:0 (Source: Crossref)

Abstract:

When modeling physical phenomena, often it is necessary to consider functions that depend on more than one variable. Therefore, if rates of changes are involved, partial derivatives of functions must be used and this leads to mathematical models that are partial differential equations. Loosely speaking, a partial differential equation is an equation that involves an unknown function of two or more variables and its partial derivatives. The following are some examples of partial differential equations:

$\begin{array}{l} u_{t} + u u_{x} & = & 0, \\ u_{x x} + u_{y y} & = & f (x, y), \\ u_{x x} + x y^{3} u_{y y} - e^{x} u_{z} + x y u & = & 0, \\ u_{t} - u_{x x} + {(u_{x})}^{2} & = & - u, \\ u_{t} + c u u_{x} + u_{x x x} & = & 0. \end{array}$

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Chapter 1: Introduction

Recommended