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This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 65M06, 65M12.The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order accuracy....

Nonstandard methods for Navier-Stokes equations

Nigel J. Cutland, Marek Capinski (1993)

Revista colombiana de matematicas

Non-Stationary Burgers Flows with Vanishing Viscosity in Bounded Domains of IR3.

Bui An Ton (1975)

Mathematische Zeitschrift

Nonstationary Marangoni convection

Alfred Wagner (1999)

Applicationes Mathematicae

Non-stationary parallel multisplitting AOR methods.

Fuster, Robert, Migallón, Violeta, Penadés, José (1996)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Nonsteady flow of water and oil through inhomogeneous porous media

H. W. Alt, E. Di Benedetto (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Nonstrictly Hyperbolic Nonlinear Systems.

Walter Craig (1987)

Mathematische Annalen

Non-symmetric elliptic operators on bounded Lipschitz domains in the plane.

Rule, David J. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Non-topological condensates in self-dual Chern-Simons gauge theory

Takashi Suzuki, Futoshi Takahashi (2004)

Banach Center Publications

This note is concerned with the recent paper "Non-topological N-vortex condensates for the self-dual Chern-Simons theory" by M. Nolasco. Modifying her arguments and statements, we show that the existence of "non-topological" multi-vortex condensates follows when the number of prescribed vortex points is greater than or equal to 2.

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