Multi-level higher order QMC Galerkin discretization for affine parametric operator equations [PDF]
, 2014 We develop a convergence analysis of a multi-level algorithm combining higher order quasi-Monte Carlo (QMC) quadratures with general Petrov-Galerkin discretizations of countably affine parametric operator equations of elliptic and parabolic type ...
Dick, Josef +3 more
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Multiplicative equations related to the affine Weyl group E$_8$
, 2017 We derive integrable equations starting from autonomous mappings with a general form inspired by the multiplicative systems associated to the affine Weyl group E$_8^{(1)}$.
Grammaticos, Basil +3 more
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Demonstratio Mathematica, 1984 This work deals with boundary value problems of the type \(Re[\overline{a(t)} w(t)]=\gamma (t)\) and \(w^+(t)=g(t) w^-(t)+h(t)\) for the general form of the systems of nonlinear equations in two dimensional domains.
openaire +2 more sources
Stresses in isostatic granular systems and emergence of force chains
, 2004 Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory?
C. Liu +11 more
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Modeling a quantum Hall system via elliptic equations [PDF]
, 2008 Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework in which to search for universal principles relevant to nanosystem modeling, and nanosystem-specific signal processing.
Sowa, Artur
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Well-posedness and regularity for a generalized fractional Cahn-Hilliard system [PDF]
, 2018 In this paper, we investigate a rather general system of two operator equations that has the structure of a viscous or nonviscous Cahn--Hilliard system in which nonlinearities of double-well type occur.
Colli, Pierluigi +2 more
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pde2path - version 2.0: faster FEM, multi-parameter continuation, nonlinear boundary conditions, and periodic domains - a short manual [PDF]
, 2014 pdepath 2.0 is an upgrade of the continuation/bifurcation package pde2path for elliptic systems of PDEs over bounded 2D domains, based on the Matlab pdetoolbox.
Dohnal, Tomas +3 more
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Localized boundary-domain singular integral equations based on harmonic parametrix for divergence-form elliptic PDEs with variable matrix coefficients [PDF]
, 2013 This is the post-print version of the Article. The official publised version can be accessed from the links below. Copyright @ 2013 Springer BaselEmploying the localized integral potentials associated with the Laplace operator, the Dirichlet, Neumann and
A.E. Taigbenu +31 more
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Lipschitz regularity for elliptic equations with random coefficients
, 2015 We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution.
Armstrong, Scott N. +1 more
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Continuity of the Feynman-Kac formula for a generalized parabolic equation
, 2016 It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an extension of the ...
Pardoux, Etienne, Rascanu, Aurel
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