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Wavelet bases for the biharmonic problem

Bímová, Daniela, Černá, Dana, Finěk, Václav (2013)

Programs and Algorithms of Numerical Mathematics

In our contribution, we study different Riesz wavelet bases in Sobolev spaces based on cubic splines satisfying homogeneous Dirichlet boundary conditions of the second order. These bases are consequently applied to the numerical solution of the biharmonic problem and their quantitative properties are compared.

Waves of Autocrine Signaling in Patterned Epithelia

C. B. Muratov, S. Y. Shvartsman (2010)

Mathematical Modelling of Natural Phenomena

A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...

Waves of excitations in heterogeneous annular region, asymmetric arrangement

András Volford, Peter Simon, Henrik Farkas (1999)

Banach Center Publications

This paper deals with the propagation of waves around a circular obstacle. The medium is heterogeneous: the velocity is smaller in the inner region and greater in the outer region. The interface separating the two regions is also circular, and the obstacle is located eccentrically inside it. The different front portraits are classified.

Wax deposition in crude oils: a new approach

Antonio Fasano, Mario Primicerio (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The complex phenomenon of solid wax deposition in wax saturated crude oils subject to thermal gradients has been treated in a number of papers under very specific assumptions (e.g. thermodynamical equilibrium between dissolved wax and the wax suspended in the oil as a crystallized phase). Here we want to consider a more general framework in which thermodynamical equilibrium may not exist, the whole system may form a gel-like structure in which the segregated solid wax has no diffusivity, the thermal...

Weak and classical solutions of equations of motion for third grade fluids

Jean Marie Bernard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper shows that the decomposition method with special basis, introduced by Cioranescu and Ouazar, allows one to prove global existence in time of the weak solution for the third grade fluids, in three dimensions, with small data. Contrary to the special case where | α 1 + α 2 | ( 24 ν β ) 1 / 2 , studied by Amrouche and Cioranescu, the H1 norm of the velocity is not bounded for all data. This fact, which led others to think, in contradiction to this paper, that the method of decomposition could not apply to...

Weak Asymptotics for Schrödinger Evolution

S. A. Denisov (2010)

Mathematical Modelling of Natural Phenomena

In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decaying potential.

Weak discrete maximum principles

Mohammad Mujalli Al-Mahameed (2005)

Archivum Mathematicum

We introduce weak discrete maximum principles for matrix equations associated with some elliptic problems. We also give an example on discrete maximum principles.

Weak entropic solution to a scalar hyperbolic-parabolic law.

Guy Vallet (2003)

RACSAM

In this paper we are interested in the Dirichlet problem of a hyperbolic-parabolic degenerate equation. Thanks to a global entropic formulation in the sense of F. Otto, we propose a result of existence and uniqueness of the entropic measure valued solution and of the entropic weak solution in the space DM2.

Weak- L p solutions for a model of self-gravitating particles with an external potential

Andrzej Raczyński (2007)

Studia Mathematica

The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- L p spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.

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