偏微分方程在数学模型中的应用

Application of Partial Differential Equations in Mathematical Models

摘要: 18世纪提出的弦振动方程、调和方程与热传导方程等著名理论，在19世纪，逐渐形成偏微分方程的一般理论。20世纪后，生产实践和科学实验提出了大量的数学物理方程的新问题。这些都说明了偏微分方程发展的迅速，以及对生活的各个方面影响。它涉及多个领域，与其他学科中的交叉学科(比如：数学物理、金融数学、生物医学和通讯工程等学科)相结合发展，建立了多种适合于相应情况的数学模型，不断地扩大了偏微分方程的研究领域，为解决数学模型的建立问题提供了又一渠道。在实际生活中的运用是非常重要的，它能为我们提供一个快捷、简便易懂的方法去解决所遇到的问题。

Abstract: In the 18th century, the famous theory of string vibration equation, harmonic equation and heat conduction equation were introduced. In the 19th century, the general theory of partial differential equations was gradually formed. After the 20th century, production practices and scientific experiments proposed a large number of new problems in mathematical physics equations. These all illustrate the rapid development of partial differential equations and the impact on life in many aspects. It involves multiple fields and is combined to develop with interdisciplinary subjects in other disciplines (e.g., mathematics physics, financial mathematics, biomedicine and communica-tion engineering, etc.), then a variety of mathematical models are established suitable for the cor-responding situation. The research field of partial differential equations is expanded continuously, providing another channel for solving the problem of establishing mathematical models. The ap-plication in real life is very important; it can provide us with a quick and easy way to solve the worry problems.