An existence result and evolutionary Γ-convergence for perturbed gradient systems View Full Text


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Article Info

DATE

2019-01-25

AUTHORS

Aras Bacho, Etienne Emmrich, Alexander Mielke

ABSTRACT

The initial-value problem for the perturbed gradient flow B(t,u(t))∈∂Ψu(t)(u′(t))+∂Et(u(t))for a.a.t∈(0,T),u(0)=u0,with a perturbation B in a Banach space V is investigated, where the dissipation potential Ψu:V→[0,+∞) and the energy functional Et:V→(-∞,+∞] are non-smooth and supposed to be convex and nonconvex, respectively. The perturbation B:[0,T]×V→V∗,(t,v)↦B(t,v) is assumed to be continuous and satisfies a growth condition. Under suitable assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semi-implicit discretization scheme with a variational approximation technique. Moreover, for perturbed gradient systems (V,Eε,Ψε,Bε) depending on a small parameter ε>0, we develop a theory of evolutionary Γ-convergence in terms of the suitable convergences of Eε, Ψε, and Bε to the limit system (V,E0,Ψ0,B0). More... »

PAGES

1-44

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-019-00484-x

DOI

http://dx.doi.org/10.1007/s00028-019-00484-x

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https://app.dimensions.ai/details/publication/pub.1111654304


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