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eBook Large-Time Behavior of Solutions of Linear Dispersive Equations (Lecture Notes in Mathematics) ePub

eBook Large-Time Behavior of Solutions of Linear Dispersive Equations (Lecture Notes in Mathematics) ePub

by Daniel B. Dix

  • ISBN: 3540634347
  • Category: Mathematics
  • Subcategory: Math Science
  • Author: Daniel B. Dix
  • Language: English
  • Publisher: Springer; 1997 edition (September 18, 1997)
  • Pages: 203
  • ePub book: 1509 kb
  • Fb2 book: 1415 kb
  • Other: lrf mbr docx rtf
  • Rating: 4.4
  • Votes: 921

Description

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dime.

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dime. Part of the Lecture Notes in Mathematics book series (LNM, volume 1668).

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. Using the method of steepest descent much new information This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension.

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Semilinear Schrodinger Equations (Courant Lecture Notes In Mathematics). Tao certainly succeeds in writing a vivid and instructional text on nonlinear dispersive partial differential equations. Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics.

Karch, Grzegorz 1999 Abstract.

Mathematical Methods in the Applied Sciences, Vol. 22, Issue. Karch, Grzegorz 1999. Self-similar large time behavior of solutions to Korteweg–de Vries–Burgers equation. Nonlinear Analysis: Theory, Methods & Applications, Vol. 35, Issue. We consider a family of dispersive equations whose simplest representative would be a Benjamin–Bona–Mahony equation with a Burger's type dissipation. The effect of possible unevenness of the bottom surface is considered and our main result gives decay rates of the solutions in Lβ(ℝ) spaces, 2 ≦ β ≦ + ∞.

2 Linear dispersive PDEs - introduction . Dispersion relations . Dispersion relations, examples. 6 6. . 3 Introduction to the Schr¨ odinger equation . Quantum mechanics . The connection between the general Lq behavior of a function and that of its Sobelev space regularity also plays an important role, quite often in nonlinear problems. Unlike the heat equation, ∂t u ∆u, which has an exponentially decaying Gaussian fundamental solution, the fundamental solution of the Schr¨odinger equation is an oscillatory Gaussian with no spatial decay. For this reason, the derivation of the solution to the initial.

This book studies the large-time asymptotic behavior of solutions of the pure initial value problem for linear dispersive equations with constant coefficients and homogeneous symbols in one space dimension. Complete matched and uniformly-valid asymptotic expansions are obtained and sharp error estimates are proved. Using the method of steepest descent much new information on the regularity and spatial asymptotics of the solutions are also obtained. Applications to nonlinear dispersive equations are discussed. This monograph is intended for researchers and graduate students of partial differential equations. Familiarity with basic asymptotic, complex and Fourier analysis is assumed.