The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise, Paperback / softback Book

The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise Paperback / softback

Part of the Lecture Notes in Mathematics series

Description

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval.

It has two stable points whose domains of attraction meet in a separating manifold with several saddle points.

Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit.

Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

Information

  • Format: Paperback / softback
  • Pages: 165 pages, 8 Illustrations, color; 1 Illustrations, black and white; XIV, 165 p. 9 illus., 8 illus.
  • Publisher: Springer International Publishing AG
  • Publication Date:
  • Category: Differential calculus & equations
  • ISBN: 9783319008271

Other Formats

£31.99

£27.69

 
Free Home Delivery

on all orders

 
Pick up orders

from local bookshops

Also in the Lecture Notes in Mathematics series   |  View all