Green's Functions: Construction and Applications: 42 (De Gruyter Studies in Mathematics, 42) - Hardcover

Über die Autorin bzw. den Autor

Yuri A. Melnikov, Middle Tennessee State University, Murfreesboro, Tennessee, USA; Max Y. Melnikov, Cumberland University, Lebanon, Tennessee, USA.

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Green's functions represent one of the classical, intensively explored, and widely implemented concepts in the area of differential equations. This monograph is looking at applied elliptic and parabolic type partial differential equations primarily in two variables. The elliptic type includes the Laplace, static Klein-Gordon, biharmonic equation, and systems simulating the static equilibrium of thin shells. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has recently emerged as a mathematical model in financial mathematics.

The intention of this book is not only to familiarize the reader with a review of classical approaches that are traditionally used for the construction of Green's functions. In addition to that, the reader will also be introduced to some nontrivial construction techniques and will be invited to a challenging research in this productive area of applied mathematics. Therefore the book is a useful source for everyone who is studying or working in fields of science, finance, or engineering that involve practical solutions of partial differential equations.