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Displaying 101 – 120 of 152

Numerical Approximations of the Dynamical System Generated by Burgers’ Equation with Neumann–Dirichlet Boundary Conditions

Edward J. Allen, John A. Burns, David S. Gilliam (2013)

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

Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...

On bifurcation and uniqueness results for some semilinear elliptic equations involving a singular potential

Manuela Chaves, Jesús García-Azorero (2006)

Journal of the European Mathematical Society

We present some results concerning the problem $- Δ u = λ \frac{u}{{| x |}^{2}} + u^{q}$ , $u > 0$ in $Ω$ , ${u |}_{\partial Ω} = 0$ , where $0 < q < (N + 2) / (N - 2)$ , $q \neq 1$ , $λ \geq 0$ and $Ω$ is a smooth bounded domain containing the origin. In particular, bifurcation and uniqueness results are discussed.

On bifurcation intervals for nonlinear eigenvalue problems

Jolanta Przybycin (1999)

Annales Polonici Mathematici

We give a sufficient condition for [μ-M, μ+M] × {0} to be a bifurcation interval of the equation u = L(λu + F(u)), where L is a linear symmetric operator in a Hilbert space, μ ∈ r(L) is of odd multiplicity, and F is a nonlinear operator. This abstract result provides an elementary proof of the existence of bifurcation intervals for some eigenvalue problems with nondifferentiable nonlinearities. All the results obtained may be easily transferred to the case of bifurcation from infinity.

On infinitely many solutions of a semilinear elliptic eigenvalue problem

Jörn Lembcke (1989)

Commentationes Mathematicae Universitatis Carolinae

On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.

Belmonte-Beitia, Juan (2008)

Mathematical Problems in Engineering

On the stationary solutions of Burgers' equation

Piotr Biler (1987)

Colloquium Mathematicae

On the structure of spectra of travelling waves.

Simon, Peter L. (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

On variational inequalities associated with the Navier-Stokes equation: Some bifurcation problems.

Le, Vy Khoi, Schmitt, Klaus (1997)

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

Period-doublings and orbit-bifurcations in symmetric systems

A. Vanderbauwhede (1989)

Banach Center Publications

Positive solution of asymptotically linear elliptic eigenvalue problems for certain differential equations of the fourth order

Jan Bochenek (1985)

Annales Polonici Mathematici

Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains.

Giacomoni, Jacques, Prajapat, Jyotshana V., Ramaswamy, Mythily (2007)

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

Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball.

Shibata, Tetsutaro (2005)

Abstract and Applied Analysis

Propagation of Singularities and Related Problems of Solidification

V. G. Danilov, G. A. Omel'yanov (1997)

Matematički Vesnik

Pullback permanence for non-autonomous partial differential equations.

Langa, Jose A., Suárez, Antonio (2002)

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

Qualitative Properties of Navier-Stokes Equations

R. Temam (1978)

Recherche Coopérative sur Programme n°25

Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions.

Eisner, Jan (2000)

Mathematica Bohemica

Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions

Jan Eisner (2000)

Mathematica Bohemica

Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.

Reaction-diffusion systems: Destabilizing effect of conditions given by inclusions II, Examples

Jan Eisner (2001)

Mathematica Bohemica

The destabilizing effect of four different types of multivalued conditions describing the influence of semipermeable membranes or of unilateral inner sources to the reaction-diffusion system is investigated. The validity of the assumptions sufficient for the destabilization which were stated in the first part is verified for these cases. Thus the existence of points at which the spatial patterns bifurcate from trivial solutions is proved.

Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities

Milan Kučera (1997)

Czechoslovak Mathematical Journal

Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.

Remarks on Krasnoselskii bifurcation theorem

Raffaele Chiappinelli (1989)

Commentationes Mathematicae Universitatis Carolinae

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