All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 88

Showing per page

B q for parabolic measures

Caroline Sweezy (1998)

Studia Mathematica

If Ω is a Lip(1,1/2) domain, μ a doubling measure on ∂ p Ω , ∂ / ∂ t - L i , i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures ω 0 , ω 1 have the property that ω 0 ∈ B q ( μ ) implies ω 1 is absolutely continuous with respect to ω 0 whenever a certain Carleson-type condition holds on the difference function of the coefficients of L 1 and L 0 . Also ω 0 ∈ B q ( μ ) implies ω 1 ∈ B q ( μ ) whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures extended...

Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type

Juan Luis Vázquez (2014)

Journal of the European Mathematical Society

We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form u ( x , t ) = t – α f ( | x | t – β ) with suitable and β . As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection...

Barriers for a class of geometric evolution problems

Giovanni Bellettini, Matteo Novaga (1997)

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

We present some general results on minimal barriers in the sense of De Giorgi for geometric evolution problems. We also compare minimal barriers with viscosity solutions for fully nonlinear geometric problems of the form u t + F ⁢ t , x , ∇ ⁡ u , ∇ 2 ⁡ u = 0 . If F is not degenerate elliptic, it turns out that we obtain the same minimal barriers if we replace F with F + , which is defined as the smallest degenerate elliptic function above F .

Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

Salah Badraoui (1999)

Applicationes Mathematicae

We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.

Behaviour of the support of the solution appearing in some nonlinear diffusion equation with absorption

Tomoeda, Kenji (2017)

Proceedings of Equadiff 14

Numerical experiments suggest interesting properties in the several fields of fluid dynamics, plasma physics and population dynamics. Among such properties, we may observe the interesting phenomena; that is, the repeated appearance and disappearance phenomena of the region penetrated by the fluid in the flow through a porous media with absorption. The model equation in two dimensional space is written in the form of the initial-boundary value problem for a nonlinear diffusion equation with the effect...

Bifurcations for Turing instability without SO(2) symmetry

Toshiyuki Ogawa, Takashi Okuda (2007)

Kybernetika

In this paper, we consider the Swift–Hohenberg equation with perturbed boundary conditions. We do not a priori know the eigenfunctions for the linearized problem since the SO ( 2 ) symmetry of the problem is broken by perturbation. We show that how the neutral stability curves change and, as a result, how the bifurcation diagrams change by the perturbation of the boundary conditions.

Bifurcations in a modulation equation for alternans in a cardiac fiber

Shu Dai, David G. Schaeffer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may lose...

Bifurcations of invariant measures in discrete-time parameter dependent cocycles

Anastasia Maltseva, Volker Reitmann (2015)

Mathematica Bohemica

We consider parameter-dependent cocycles generated by nonautonomous difference equations. One of them is a discrete-time cardiac conduction model. For this system with a control variable a cocycle formulation is presented. We state a theorem about upper Hausdorff dimension estimates for cocycle attractors which includes some regulating function. We also consider the existence of invariant measures for cocycle systems using some elements of Perron-Frobenius theory and discuss the bifurcation of parameter-dependent...

Currently displaying 1 – 20 of 88

Page 1 Next