NDLI logo
  • Content
  • Similar Resources
  • Metadata
  • Cite This
  • Log-in
  • Fullscreen
Log-in
Do not have an account? Register Now
Forgot your password? Account recovery
  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 55
  3. Calculus of Variations and Partial Differential Equations : Volume 55, Issue 3, June 2016
  4. Relaxation times for atom dislocations in crystals
Loading...

Please wait, while we are loading the content...

Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 6, December 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 5, October 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 4, August 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 3, June 2016
On Newton equations which are totally integrable at infinity
Existence of minimal surfaces of arbitrarily large Morse index
Dichotomy of stable radial solutions of $$-\Delta u=f(u)$$ outside a ball
Existence of very weak solutions to elliptic systems of p-Laplacian type
Blow-up of the mean curvature at the first singular time of the mean curvature flow
Existence and concentration of solution for a class of fractional elliptic equation in $$\mathbb {R}^N$$ via penalization method
A strictly convex Sobolev function with null Hessian minors
Measure contraction properties of Carnot groups
Rigidity of stable minimal hypersurfaces in asymptotically flat spaces
$$\sigma _2$$ -Diffeomorphisms between 4-dimensional annuli
On a generalization of $$L^p$$ -differentiability
On the Euler-Lagrange equation of a functional by Pólya and Szegö
Qualitative properties of solutions to mixed-diffusion bistable equations
An Allard type regularity theorem for varifolds with a Hölder condition on the first variation
Lower semicontinuity for an integral functional in BV
Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations
Classification of solutions to Toda systems of types C and B with singular sources
Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group
Multi-bump solutions for Choquard equation with deepening potential well
The obstacle problem for nonlinear integro-differential operators
The curve shortening problem associated to a density
The $$ L^2 $$ -gradient of decomposed Möbius energies
Front blocking and propagation in cylinders with varying cross section
Interior gradient estimates for quasilinear elliptic equations
Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case
Relaxation times for atom dislocations in crystals
Cahn–Hilliard–Navier–Stokes systems with moving contact lines
Homogenization of integral energies under periodically oscillating differential constraints
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 2, April 2016
Calculus of Variations and Partial Differential Equations : Volume 55, Issue 1, February 2016
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

Similar Documents

...
The extremal solution for the fractional Laplacian

Article

...
Traveling wave solutions to some reaction diffusion equations with fractional Laplacians

Article

...
Multiple solutions for nonhomogeneous Schrödinger–Kirchhoff type equations involving the fractional p-Laplacian in $${\mathbb {R}}^N$$

Article

...
The obstacle problem for nonlinear integro-differential operators

Article

...
Ground state solutions of scalar field fractional Schrödinger equations

Article

...
Fractional eigenvalues

Article

...
Regularity for fully nonlinear nonlocal parabolic equations with rough kernels

Article

...
Large time behavior of periodic viscosity solutions for uniformly parabolic integro-differential equations

Article

...
Infinitely many non-radial solutions for fractional Nirenberg problem

Article

Relaxation times for atom dislocations in crystals

Content Provider SpringerLink
Author Patrizi, Stefania Valdici, Enrico
Copyright Year 2016
Abstract We study the relaxation times for a parabolic differential equation whose solution represents the atom dislocation in a crystal. The equation that we consider comprises the classical Peierls–Nabarro model as a particular case, and it allows also long range interactions. It is known that the dislocation function of such a model has the tendency to concentrate at single points, which evolve in time according to the external stress and a singular, long range potential. Depending on the orientation of the dislocation function at these points, the potential may be either attractive or repulsive, hence collisions may occur in the latter case and, at the collision time, the dislocation function does not disappear. The goal of this paper is to provide accurate estimates on the relaxation times of the system after collision. More precisely, we take into account the case of two and three colliding points, and we show that, after a small transition time subsequent to the collision, the dislocation function relaxes exponentially fast to a steady state. In this sense, the system exhibits two different decay behaviors, namely an exponential time decay versus a polynomial decay in the space variables (and these two homogeneities are kept separate during the time evolution).
Ending Page 44
Page Count 44
Starting Page 1
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3
Volume Number 55
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2016-06-14
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Integro-differential operators Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Crystals Fractional partial differential equations Integro-partial differential equations Crystalline structure
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
  • About
  • Disclaimer
  • Feedback
  • Sponsor
  • Contact
  • Chat with Us
About National Digital Library of India (NDLI)
NDLI logo

National Digital Library of India (NDLI) is a virtual repository of learning resources which is not just a repository with search/browse facilities but provides a host of services for the learner community. It is sponsored and mentored by Ministry of Education, Government of India, through its National Mission on Education through Information and Communication Technology (NMEICT). Filtered and federated searching is employed to facilitate focused searching so that learners can find the right resource with least effort and in minimum time. NDLI provides user group-specific services such as Examination Preparatory for School and College students and job aspirants. Services for Researchers and general learners are also provided. NDLI is designed to hold content of any language and provides interface support for 10 most widely used Indian languages. It is built to provide support for all academic levels including researchers and life-long learners, all disciplines, all popular forms of access devices and differently-abled learners. It is designed to enable people to learn and prepare from best practices from all over the world and to facilitate researchers to perform inter-linked exploration from multiple sources. It is developed, operated and maintained from Indian Institute of Technology Kharagpur.

Learn more about this project from here.

Disclaimer

NDLI is a conglomeration of freely available or institutionally contributed or donated or publisher managed contents. Almost all these contents are hosted and accessed from respective sources. The responsibility for authenticity, relevance, completeness, accuracy, reliability and suitability of these contents rests with the respective organization and NDLI has no responsibility or liability for these. Every effort is made to keep the NDLI portal up and running smoothly unless there are some unavoidable technical issues.

Feedback

Sponsor

Ministry of Education, through its National Mission on Education through Information and Communication Technology (NMEICT), has sponsored and funded the National Digital Library of India (NDLI) project.

Contact National Digital Library of India
Central Library (ISO-9001:2015 Certified)
Indian Institute of Technology Kharagpur
Kharagpur, West Bengal, India | PIN - 721302
See location in the Map
03222 282435
Mail: support@ndl.gov.in
Sl. Authority Responsibilities Communication Details
1 Ministry of Education (GoI),
Department of Higher Education
Sanctioning Authority https://www.education.gov.in/ict-initiatives
2 Indian Institute of Technology Kharagpur Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project https://www.iitkgp.ac.in
3 National Digital Library of India Office, Indian Institute of Technology Kharagpur The administrative and infrastructural headquarters of the project Dr. B. Sutradhar  bsutra@ndl.gov.in
4 Project PI / Joint PI Principal Investigator and Joint Principal Investigators of the project Dr. B. Sutradhar  bsutra@ndl.gov.in
Prof. Saswat Chakrabarti  will be added soon
5 Website/Portal (Helpdesk) Queries regarding NDLI and its services support@ndl.gov.in
6 Contents and Copyright Issues Queries related to content curation and copyright issues content@ndl.gov.in
7 National Digital Library of India Club (NDLI Club) Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach clubsupport@ndl.gov.in
8 Digital Preservation Centre (DPC) Assistance with digitizing and archiving copyright-free printed books dpc@ndl.gov.in
9 IDR Setup or Support Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops idr@ndl.gov.in
I will try my best to help you...
Cite this Content
Loading...