Mathematical Models and Methods in Applied SciencesAccepted Papers No AccessThe Weighted Inertia-Energy-Dissipation PrincipleUlisse StefanelliUlisse Stefanellihttps://doi.org/10.1142/S0218202525400019Cited by:0 (Source: Crossref) Next AboutFiguresReferencesRelatedDetailsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend Library ShareShare onFacebookTwitterLinked InRedditEmail Cite Recommend Remember check out the Most Cited Articles! View our Modelling books Featuring...

The celebrated Brezis–Ekeland principle [C. R. Acad. Sci. Paris Ser. A-B, 282 (1976), pp. Ai, A1197–A1198, Aii, and A971–A974] characterizes trajectories of nonautonomous gradient flows convex functionals as solutions to suitable minimization problems. This note extends this characterization doubly nonlinear evolution equations driven by potentials. is exploited in order establish approximation results for flows, equations, rate-independent evolutions.

This paper addresses two-dimensional crystallization in the square lattice. A suitable configurational potential featuring both two- and three-body short-ranged particle interactions is considered. We prove that every ground state a connected subset of Moreover, we discuss global geometry states their optimality terms discrete isoperimetric inequalities on graph. Eventually, study aspect ratio quantitatively emergence macroscopic Wulff shape as number particles grows.

This paper addresses a three-dimensional model for isothermal stress-induced transformation in shape-memory polycrystalline materials. We treat the problem within framework of energetic formulation rate-independent processes and investigate existence continuous dependence issues at both constitutive relation quasi-static evolution level. Moreover, we focus on time space approximation as well regularization parameter asymptotics.

We provide a rigorous justification of the classical linearization approach in plasticity. By taking small-deformations limit, we prove via \Gamma -convergence for rate-independent processes that energetic solutions quasi-static finite-strain elastoplasticity system converge to unique strong solution linearized elastoplasticity.

.A model of saturated hyperelastic porous solids at large strains is formulated and analyzed. The material response assumed to be a viscoelastic Kelvin–Voigt type, inertial effects are considered, too. flow the diffusant driven by gradient chemical potential coupled mechanics via occurrence swelling squeezing. Buoyancy due evolving mass density in gravity field covered. Higher-order viscosity also included, allowing for physically relevant stored energies local invertibility deformation....

Abstract We investigate the optimal arrangements of two planar sets given volume which are minimizing <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi mathvariant="normal">ℓ</m:mi> <m:mn>1</m:mn> </m:msub> </m:math> {\ell_{1}} double-bubble interaction functional. The latter features a competition between minimization perimeters and maximization their interface. problem in its full generality for finite perimeter, by considering whole range possible intensities all...

This paper addresses a doubly nonlinear parabolic inclusion of the form <p align="center"> $\mathcal A (u_t)+\mathcal B (u)$ ∋ f. align="left" class="times"> Existence solution is proved under suitable monotonicity, coercivity, and structure assumptions on operators $ B$, which in particular are both supposed to be subdifferentials functionals $L^2(\Omega)$. Since <i> unbounded</i> included analysis, this theory partly extends Colli & Visintin's work [24]. Moreover, additional hypotheses...

We analyze the finite-strain Poynting–Thomson viscoelastic model. In its linearized small-deformation limit, this corresponds to serial connection of an elastic spring and a Kelvin–Voigt element. case, total deformation body results from composition two maps, describing element one, respectively. prove existence suitably weak solutions by time-discretization approach based on incremental minimization. Moreover, we rigorous linx earization result, showing that corresponding small-strain model...

Abstract Rate‐independent evolution driven by non‐convex potentials is nature non‐smooth and some weak solvability notions have been recently advanced. This note intended to contribute this discussion proposing a variational characterization of rate‐independent based on principle maximal dissipation criterion. The resulting novel solution notion assessed in an elementary yet critical scalar case (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed Mielke and Ortiz [ESAIM: COCV 14 (2008) 494-516].In particular, we focus on gradient flows in Hilbert spaces.The main result is convergence minimizers approximate these unique solution flow.Sharp rates are provided analysis combined with timediscretization.Applications theory various classes parabolic PDE problems presented.In two examples microstructure from [S.

We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in finite-time case.