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Stochasticp-adic equations of mathematical physics
Theoretical and Mathematical Physics, 1999The author introduces several classes of complex-valued stochastic processes with \(p\)-adic time parameters. The basic process is the \(p\)-adic white noise, a Gaussian generalized stochastic process \(\Phi (\varphi)\), \(\varphi \in \mathcal D(Q_p)\) (the Schwartz-Bruhat space of test functions), with zero mean and the covariation \[ \mathbf E\Phi ...
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Mathematical Physics with Differential Equations
2023Abstract This book presents a broad range of fundamental topics in theoretical and mathematical physics based on the viewpoint of differential equations. The subject areas covered include classical and quantum many-body problems, thermodynamics, electromagnetism, magnetic monopoles, special relativity, gauge field theories, general ...
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Partial Differential Equations of Mathematical Physics
2016If an unknown function of several variables and its partial derivatives are combined in an equation, the latter is called a partial differential equation (PDE ) . Several times above we have come across such PDEs when dealing with functions of several variables. For instance, in Sect.
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Conditional symmetry of the equations of nonlinear mathematical physics
Ukrainian Mathematical Journal, 1991The author deals with conditional symmetry of partial differential equations --- roughly speaking with the symmetry of certain subset of solutions. Such a symmetry can be used in generalization of invariance principle, reduction and linearization of equations and in the process of obtaining solutions, which cannot be obtained by some classical methods.
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Equations of Mathematical Physics
Mathematics of Computation, 1972Vidar Thomee, V. S. Vladimirov
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A GEOMETRIC STUDY OF SOME EQUATIONS OF MATHEMATICAL PHYSICS
International Journal of Geometric Methods in Modern Physics, 2012We introduce geometric structures (connections, pseudo-Riemannian metrics) adapted to some fundamental problems of Differential Geometry, and find geometrical characteristics associated to equations of Mathematical Physics. Also, we introduce a geometric study of some boundary problems.
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Equations of Mathematical Physics
American Journal of Physics, 1971V. S. Vladimirov, Franklin E. Schroeck
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Linear Random Operator Equations in Mathematical Physics. II
Journal of Mathematical Physics, 1971This paper is a continuation of Paper I [J. Math. Phys. 11, 1069 (1970)]. A general expression is determined for the stochastic Green's function (SGF) for two-point correlation functions, and various useful relationships are determined between the stochastic Green's functions for various statistical measures and between the stochastic Green's functions,
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Equations in Mathematical Physics
2001Victor P. Pikulin, Stanislav I. Pohozaev
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Partial Differential Equations of Mathematical Physics
1998Chapters 2 through 4 of this text developed solution methods for physical problems that are governed by ordinary differential equations. The purpose of Chapters 7 through 9 is to extend these methods to problems that are governed by partial differential equations.
Grant B. Gustafson, Calvin H. Wilcox
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