Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization

Etienne Emmrich; David Siska

doi:10.1016/j.jde.2013.07.065

Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization

Etienne Emmrich^*, David Siska

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

Global existence of solutions for a class of second-order evolution equations with damping is shown by proving convergence of a full discretization. The discretization combines a fully implicit time stepping with a Galerkin scheme. The operator acting on the zero-order term is assumed to be a potential operator where the potential may be nonconvex. A linear, symmetric operator is assumed to be acting on the first-order term. Applications arise in nonlinear viscoelasticity and elastodynamics. (C) 2013 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	3719-3746
Number of pages	28
Journal	Journal of Differential Equations
Volume	255
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2013.07.065
Publication status	Published - 15 Nov 2013

Keywords / Materials (for Non-textual outputs)

Evolution equation of second order
Elastodynamics
Nonconvex potential
Full discretization
Convergence
SHAPE-MEMORY ALLOYS
GLOBAL REGULAR SOLUTIONS
FINITE-ELEMENT SPACES
TIME DISCRETIZATION
NONLINEAR VISCOELASTICITY
DIFFERENTIAL-EQUATIONS
PHASE-TRANSITIONS
WEAK SOLUTIONS
ELASTODYNAMICS
STABILITY

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10.1016/j.jde.2013.07.065

Evolution equations of second order with nonconvex potential and linear damping existence via convergence of a full discretizationAccepted author manuscript, 228 KB

http://www.sciencedirect.com/science/article/pii/S0022039613003409

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title = "Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization",

abstract = "Global existence of solutions for a class of second-order evolution equations with damping is shown by proving convergence of a full discretization. The discretization combines a fully implicit time stepping with a Galerkin scheme. The operator acting on the zero-order term is assumed to be a potential operator where the potential may be nonconvex. A linear, symmetric operator is assumed to be acting on the first-order term. Applications arise in nonlinear viscoelasticity and elastodynamics. (C) 2013 Elsevier Inc. All rights reserved.",

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author = "Etienne Emmrich and David Siska",

year = "2013",

month = nov,

day = "15",

doi = "10.1016/j.jde.2013.07.065",

language = "English",

volume = "255",

pages = "3719--3746",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press",

number = "10",

}

TY - JOUR

T1 - Evolution equations of second order with nonconvex potential and linear damping

T2 - existence via convergence of a full discretization

AU - Emmrich, Etienne

AU - Siska, David

PY - 2013/11/15

Y1 - 2013/11/15

N2 - Global existence of solutions for a class of second-order evolution equations with damping is shown by proving convergence of a full discretization. The discretization combines a fully implicit time stepping with a Galerkin scheme. The operator acting on the zero-order term is assumed to be a potential operator where the potential may be nonconvex. A linear, symmetric operator is assumed to be acting on the first-order term. Applications arise in nonlinear viscoelasticity and elastodynamics. (C) 2013 Elsevier Inc. All rights reserved.

AB - Global existence of solutions for a class of second-order evolution equations with damping is shown by proving convergence of a full discretization. The discretization combines a fully implicit time stepping with a Galerkin scheme. The operator acting on the zero-order term is assumed to be a potential operator where the potential may be nonconvex. A linear, symmetric operator is assumed to be acting on the first-order term. Applications arise in nonlinear viscoelasticity and elastodynamics. (C) 2013 Elsevier Inc. All rights reserved.

KW - Evolution equation of second order

KW - Elastodynamics

KW - Nonconvex potential

KW - Full discretization

KW - Convergence

KW - SHAPE-MEMORY ALLOYS

KW - GLOBAL REGULAR SOLUTIONS

KW - FINITE-ELEMENT SPACES

KW - TIME DISCRETIZATION

KW - NONLINEAR VISCOELASTICITY

KW - DIFFERENTIAL-EQUATIONS

KW - PHASE-TRANSITIONS

KW - WEAK SOLUTIONS

KW - ELASTODYNAMICS

KW - STABILITY

U2 - 10.1016/j.jde.2013.07.065

DO - 10.1016/j.jde.2013.07.065

M3 - Article

SN - 0022-0396

VL - 255

SP - 3719

EP - 3746

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

Evolution equations of second order with nonconvex potential and linear damping: existence via convergence of a full discretization

Abstract / Description of output

Keywords / Materials (for Non-textual outputs)

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