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Parabolic Equations with Irregular Data and Related Issues

2019-06-17 Mathematics
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Release : 2019-06-17
Genre : Mathematics
Kind : eBook
Book Rating : 50X/5 ( reviews)

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Book Synopsis Parabolic Equations with Irregular Data and Related Issues by : Claude Le Bris

Download or read book Parabolic Equations with Irregular Data and Related Issues written by Claude Le Bris. This book was released on 2019-06-17. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Parabolic Partial Differential Equations with Irregular Data. Related Issues. Application to Stochastic Differential Equations

2015
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Release : 2015
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Book Synopsis Parabolic Partial Differential Equations with Irregular Data. Related Issues. Application to Stochastic Differential Equations by : Claude Le Bris

Download or read book Parabolic Partial Differential Equations with Irregular Data. Related Issues. Application to Stochastic Differential Equations written by Claude Le Bris. This book was released on 2015. Available in PDF, EPUB and Kindle. Book excerpt: "We study the existence and the uniqueness of the solution to parabolic type equations with irregular coefficients and/or initial conditions. The coefficients considered in the equation typically belong to Lebesgue or Sobolev spaces, the initial condition may be only Lebesgue integrable, the second order term in the equation may be degenerate. The arguments elaborate on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations. The connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation is examined. We in particular follow up on two previous articles. These notes, written up jointly by the two authors, lay out the background on the various issues and present the recent results obtained by the second author. They are an expanded version of the lectures delivered at Collège de France during the academic year 2012-13." [résumé de la page de titre].

Parabolic Equations with Irregular Data and Related Issues

2019-06-17 Mathematics
Download Parabolic Equations with Irregular Data and Related Issues PDF Online Free

Author :
Release : 2019-06-17
Genre : Mathematics
Kind : eBook
Book Rating : 140/5 ( reviews)

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Book Synopsis Parabolic Equations with Irregular Data and Related Issues by : Claude Le Bris

Download or read book Parabolic Equations with Irregular Data and Related Issues written by Claude Le Bris. This book was released on 2019-06-17. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

Parabolic Equations on an Infinite Strip

2017-10-02 Mathematics
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Release : 2017-10-02
Genre : Mathematics
Kind : eBook
Book Rating : 900/5 ( reviews)

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Book Synopsis Parabolic Equations on an Infinite Strip by : Watson

Download or read book Parabolic Equations on an Infinite Strip written by Watson. This book was released on 2017-10-02. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.

Qualitative Theory of Parabolic Equations, Part 1

2011-09-06 Mathematics
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Release : 2011-09-06
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)

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Book Synopsis Qualitative Theory of Parabolic Equations, Part 1 by : T. I. Zelenyak

Download or read book Qualitative Theory of Parabolic Equations, Part 1 written by T. I. Zelenyak. This book was released on 2011-09-06. Available in PDF, EPUB and Kindle. Book excerpt: In the qualitative theory of ordinary differential equations, the Liapunov method plays a fundamental role. To use their analogs for the analysis of stability of solutions to parabolic, hyperparabolic, and other nonclassical equations and systems, time-invariant a priori estimates have to be devised for solutions. In this publication only parabolic problems are considered. Here lie, mainly, the problems which have been investigated most thoroughly --- the construction of Liapunov functionals which naturally generalize Liapunov functions for nonlinear parabolic equations of the second order with one spatial variable. The authors establish stabilizing solutions theorems, and the necessary and sufficient conditions of general and asymptotic stability of stationary solutions, including the so-called critical case. Attraction domains for stable solutions of mixed problems for these equations are described. Furthermore, estimates for the number of stationary solutions are obtained.

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