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Functional Integration and Partial Differential Equations
-
Mark Iosifovich Freidlin
Language:
English
Published/Copyright:
2016
About this book
This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.
Topics
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Frontmatter
i -
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CONTENTS
v -
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PREFACE
viii -
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INTRODUCTION
1 -
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I. STOCHASTIC DIFFERENTIAL EQUATIONS AND RELATED TOPICS
16 -
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II. REPRESENTATION OF SOLUTIONS OF DIFFERENTIAL EQUATIONS AS FUNCTIONAL INTEGRALS AND THE STATEMENT OF BOUNDARY V A LU E PROBLEMS
117 -
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III. BOUNDARY VALUE PROBLEMS FOR EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM
184 -
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IV. SMALL PARAMETER IN SECOND-ORDER ELLIPTIC DIFFERENTIAL EQUATIONS
264 -
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V. QUASI-LINEAR PARABOLIC EQUATIONS WITH NON-NEGATIVE CHARACTERISTIC FORM
352 -
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VI. QUASI-LINEAR PARABOLIC EQUATIONS WITH SMALL PARAMETER. WAVE FRONTS PROPAGATION
395 -
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VII. WAVE FRONT PROPAGATION IN PERIODIC AND RANDOM MEDIA
478 -
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LIST OF NOTATIONS
531 -
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REFERENCES
534 -
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Backmatter
546
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 20, 2016
eBook ISBN:
9781400881598
Pages and Images/Illustrations in book
eBook ISBN:
9781400881598
Keywords for this book
Equation; Boundary value problem; Coefficient; Markov process; Differential equation; Theorem; Wiener process; Central limit theorem; Sign (mathematics); Dirichlet problem; Stochastic calculus; Linear differential equation; Derivative; Elliptic partial differential equation; Degeneracy (mathematics); Diffusion process; Lipschitz continuity; Integral equation; Partial differential equation; Ordinary differential equation; Stochastic differential equation; Continuous function (set theory); Elliptic operator; Probabilistic method; Mean value theorem; Girsanov theorem; Eigenfunction; Itô's lemma; Feynman–Kac formula; Direct method in the calculus of variations; Eigenvalues and eigenvectors; Modulus of continuity; Dirichlet boundary condition; Analytic continuation; Iterated logarithm; Differential operator; Continuous function; Laplace's equation; Fokker–Planck equation; Gaussian measure; Probability; Navier–Stokes equations; Schrödinger equation; Variable (mathematics); Existence theorem; Dimension (vector space); Hessian matrix; Simultaneous equations; Characteristic function (probability theory); Laplace operator; Smoothness; Exponential function; Parameter; Lebesgue measure; Limit (mathematics); Uniqueness theorem; Invariant measure; Integral curve; Joint probability distribution; A priori estimate; Bounded function; State-space representation; Regularization (mathematics); Moment (mathematics); Nonlinear system; Poisson kernel; Random function; Monotonic function; Markov chain; Measure (mathematics)
Audience(s) for this book
For an expert adult audience, including professional development and academic research
