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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 51
  3. Calculus of Variations and Partial Differential Equations : Volume 51, Issue 3-4, November 2014
  4. Existence of solutions to the Kobayashi–Warren–Carter system
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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 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 51, Issue 3-4, November 2014
Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces
Regularity of minimal hypersurfaces with a common free boundary
Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem
Global Calderón–Zygmund theory for nonlinear parabolic systems
Intrinsically $$p$$ -biharmonic maps
Existence of solutions to the Kobayashi–Warren–Carter system
A quantitative estimate for mappings of bounded inner distortion
Derivation of a homogenized nonlinear plate theory from 3d elasticity
Spherical symmetrization and the first eigenvalue of geodesic disks on manifolds
Semiclassical limits of ground state solutions to Schrödinger systems
Infinitely many positive solutions for nonlinear equations with non-symmetric potentials
A sharp strong maximum principle and a sharp unique continuation theorem for singular minimal hypersurfaces
Analyse sur un demi-espace hyperbolique et poly-homogénéité locale
Local gradient estimate for harmonic functions on Finsler manifolds
Biharmonic elliptic problems involving the 2nd Hessian operator
Compact stable hypersurfaces with free boundary in convex solid cones with homogeneous densities
Global existence of weak solution for the 2-D Ericksen–Leslie system
Partial Sobolev spaces and anisotropic smectic liquid crystals
Calculus of Variations and Partial Differential Equations : Volume 51, Issue 1-2, September 2014
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

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Existence of solutions to the Kobayashi–Warren–Carter system

Content Provider SpringerLink
Author Moll, Salvador Shirakawa, Ken
Copyright Year 2013
Abstract In this paper, a coupled system of two parabolic type initial-boundary value problems is considered. The system is known as the Kobayashi–Warren–Carter model of grain boundary motion in a polycrystal. Kobayashi–Warren–Carter model is derived as a gradient descent flow of an energy functional, which is called “free-energy”, with respect to two unknown variables and it involves a weighted-unknown dependent total variation term. The main goal of this paper is to obtain existence of solutions to this system. We solve the problem by means of a time-discretization of a relaxed system and a highly non-trivial passage to the limit. We point out that our time-discretization method is effective not only for the original Kobayashi–Warren–Carter system but also for its relaxed versions. Therefore, we provide a uniform approach for obtaining solutions to systems associated with this model.
Ending Page 656
Page Count 36
Starting Page 621
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 3-4
Volume Number 51
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2013-12-05
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Systems of parabolic variational inequalities Partial differential equations with measure Initial value problems for second-order parabolic systems Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Free boundary problems Singular parabolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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