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Separation of Variables and Exact Solutions to Nonlinear PDEsкнига
- Авторы: Polyanin A.D., Zhurov A.I.
- Год издания: 2022
- Издательство: CRC Press
- Местоположение издательства: Boca Raton, United States
- Объём: 401 страниц
- ISBN: 978-0-367-48689-1
- Монография
- DOI: 10.1201/9781003042297
- Аннотация: The book is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations. It also presents the direct methodof symmetry reductions (in many respects akin to the methods of functional separation of variables) and its more general version based on the splitting principle in sufficient detail. Besides, it describes the differentialconstraint method, which generalizes many other exact methods.The text involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematicalphysics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology,biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest as they can be used to assess numerical methods' accuracy for solving the corresponding initial-boundary value problems. The book contains much new material previously unpublished in monographs.The book is intended for a broad audience of scientists, university teachers, engineers, postgraduate students, and graduate students that specialize in applied and computational mathematics, mathematical and theoretical physics, mechanics, control theory, biology, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering specialcourses, and for practical training.
- Добавил в систему: Полянин Андрей Дмитриевич