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Contemporary developments in continuum mechanics and partial differential equations
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The article was published on 1978-01-01 and is currently open access. It has received 53 citations till now. The article focuses on the topics: Continuum mechanics & Partial differential equation.read more
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Fine phase mixtures as minimizers of energy
TL;DR: In this article, the authors explore a theoretical approach to these fine phase mixtures based on the minimization of free energy and show that the α-phase breaks up into triangular domains called Dauphine twins which become finer and finer in the direction of increasing temperature.
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Thomas-fermi and related theories of atoms and molecules
TL;DR: In this paper, a summary of what is know rigorously about Thomas-Fermi (TF) theory with and without the Dirac and von Weizsacker corrections is given.
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On the Well-Posedness of the Kirchhoff String
Alberto Arosio,Stefano Panizzi +1 more
TL;DR: In this article, the Cauchy problem for the quasilinear hyperbolic integro-differential equation is considered for the case of a quasileinear QDE.
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A class of general algorithms for multi-scale analyses of heterogeneous media
Kenjiro Terada,Noboru Kikuchi +1 more
TL;DR: In this article, a two-scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements, which can be unified in association with the homogenization procedure for general nonlinear problems.
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On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
TL;DR: This work approximate the solutions of an initial- and boundary-value problem for nonlinear Schrödinger equations by two fully discrete finite element schemes based on the standard Galerkin method in space and two implicit schemes, each of which proves L2 error bounds of optimal order of accuracy.