Differential Equations - Geometry, Symmetries and Integrability
Differential Equations - Geometry, Symmetries and Integrability

Author: Boris Kruglikov

Publisher: Springer Science & Business Media

Published: 2009-07-24

Total Pages: 394

ISBN-13: 3642008739

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The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Differential Equations
Differential Equations

Author: O.A. Oleinik

Publisher: CRC Press

Published: 2019-08-16

Total Pages: 522

ISBN-13: 1000725197

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Part II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.