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Displaying 21 – 36 of 36

Vertical compaction in a faulted sedimentary basin

Gérard Gagneux, Roland Masson, Anne Plouvier-Debaigt, Guy Vallet, Sylvie Wolf (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....

Vertical compaction in a faulted sedimentary basin

Gérard Gagneux, Roland Masson, Anne Plouvier-Debaigt, Guy Vallet, Sylvie Wolf (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy's law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....

Very weak solutions of nonlinear subelliptic equations.

Zatorska-Goldstein, Anna (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

Very weak solutions of the stationary Stokes equations in unbounded domains of half space type

Reinhard Farwig, Jonas Sauer (2015)

Mathematica Bohemica

We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as $ℝ_{+}^{n}$ , bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of $ℝ_{+}^{n}$ , and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous...

Verzweigung und Stabilität von Lösungen semilinearer elliptischer Randwertprobleme.

J. Scheurle, K. Kirchgässner (1975/1976)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Věta o reciprocitě pro přechodné jevy

Ivan Šantavý (1957)

Aplikace matematiky

Visco-elastic-plastic modelling

Koppová, Jana, Minárová, Mária, Sumec, Jozef (2017)

Proceedings of Equadiff 14

In this paper we deal with the mathematical modelling of rheological models with applications in various engineering disciplines and industry. We study the mechanical response of visco-elasto-plastic materials. We describe the basic rheological elements and focus our attention to the specific model of concrete, for which we derive governing equations and discuss its solution. We provide an application of rheological model involving rigid-plastic element as well - mechanical and mathematical model...

Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem

Claudia Lederman, Noemi Wolanski (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Viscosity solutions of elliptic partial differential equations.

Jensen, Robert R. (1998)

Documenta Mathematica

Viscosity solutions of nonlinear systems of degenerated elliptic equations of second order.

Liu, Weian, Chen, Hua (2000)

Zeitschrift für Analysis und ihre Anwendungen

Viscosity subsolutions and supersolutions for non-uniformly and degenerate elliptic equations

Aris S. Tersenov (2009)

Archivum Mathematicum

In the present paper we study the Dirichlet boundary value problem for quasilinear elliptic equations including non-uniformly and degenerate ones. In particular, we consider mean curvature equation and pseudo p-Laplace equation as well. It is well-known that the proof of the existence of continuous viscosity solutions is based on Ishii’s implementation of Perron’s method. In order to use this method one has to produce suitable subsolution and supersolution. Here we introduce new methods to construct...

Von Neumann analysis of linearized discrete Tzitzeica PDE.

Udrişte, Constantin, Arsinte, Vasile, Cipu, Corina (2010)

Balkan Journal of Geometry and its Applications (BJGA)

Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation

Sylvia Serfaty (2007)

Journal of the European Mathematical Society

We study vortices for solutions of the perturbed Ginzburg–Landau equations $Δ u + (u / ε^{2}) {(1 - | u |}^{2}) = f_{ε}$ where $f_{ε}$ is estimated in $L^{2}$ . We prove upper bounds for the Ginzburg–Landau energy in terms of $∥ f_{ε} ∥_{L^{2}}$ , and obtain lower bounds for $∥ f_{ε} ∥_{L^{2}}$ in terms of the vortices when these form “unbalanced clusters” where $\sum_{i} d_{i}^{2} \neq {(\sum_{i} d_{i})}^{2}$ . These results will serve in Part II of this paper to provide estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat flow, which allow one to study various phenomena occurring in this flow, including...

Vortex dans les condensats de Bose Einstein

Amandine Aftalion (2004/2005)

Séminaire Équations aux dérivées partielles

Vortex rings for the Gross-Pitaevskii equation

Fabrice Bethuel, G. Orlandi, Didier Smets (2004)

Journal of the European Mathematical Society

We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension $N \geq 3$ . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if $N = 3$ ).

Vortices in Ginzburg-Landau equations.

Bethuel, Fabrice (1998)

Documenta Mathematica

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