Publications related to Initial value problem

Analytical approximations for the collapse of an empty spherical bubble

The Rayleigh equation 3/2 (R) over dot + R(R) double over dot + p rho(-1) = 0 with initial conditions R(0) = R-0, (R) over dot(0) = 0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and ...

2012

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

Joachim Krieger

In this paper we prove the global in time well-posedness of the following non-local diffusion equation with

\alpha\, \varepsilon [0, 2/3)

:

\partial_tu=\{(-\Delta)^{-1}u\}\Delta u+\alpha u^2, \,\, u(t=0)=u_0

. The initial condition

u_0

is positive, rad ...

2012

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec, Javier Gomez Serrano

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

World Scientific Publishing2012

A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities

Dominique Bonvin, Grégory François

Run-to-run control is a technique that exploits the repetitive nature of processes to iteratively adjust the inputs and drive the run-end outputs to their reference values. It can be used to control both static and finite-time dynamic systems. Although the ...

American Chemical Society2011

Nonlinear quasisteady state benchmark of global gyrokinetic codes

Laurent Villard, Stephan Brunner, Ben McMillan, Xavier Lapillonne

Two global gyrokinetic codes are benchmarked against each other by comparing simulation results in the case of ion temperature gradient driven turbulence, in the adiabatic electron response limit The two codes are the Eulerian code GENE and the Lagrangian ...

American Institute of Physics2010

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec, Javier Gomez Serrano

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

2010

Construction of a High Order Fluid-Structure Interaction Solver

Gonçalo Pena

Accuracy is critical if we are to trust simulation predictions. In settings such as ﬂuid- structure interaction it is all the more important to obtain reliable results to understand, for example, the impact of pathologies on blood ﬂows in the cardiovascula ...

Elsevier2010

Lectures on the Orbital Stability of Standing Waves and Application to the Nonlinear Schrodinger Equation

Charles Stuart

In the first part of these notes, we deal with first order Hamiltonian systems in the form Ju'(t) = del H(u(t)) where the phase space X may be in infinite dimensional so as to accommodate some partial differential equations. The Hamiltonian H is an element ...

Birkhäuser-Verlag, Springer2008

Steady-state Solutions in Mathematical Models of Atrial Cell Electrophysiology and their Stability

Vincent Jacquemet

The steady states of the Fenton–Karma, the Courtemanche and the Nygren cell models were studied by determining the fixed points of the dynamical system describing their cell kinetics. The linear stability of the fixed points was investigated, as well as th ...

2007

Uncertainty analysis for the steady-state flows in a dual throat nozzle

Jan Sickmann Hesthaven

It is well known that the steady state of an isentropic flow in a dual-throat nozzle with equal throat areas is not unique. In particular there is a possibility that the flow contains a shock wave, whose location is determined solely by the initial conditi ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2005

Initial value problem

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Analytical approximations for the collapse of an empty spherical bubble

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

The Bounded Confidence Model Of Opinion Dynamics

A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities

Nonlinear quasisteady state benchmark of global gyrokinetic codes

The Bounded Confidence Model Of Opinion Dynamics

Construction of a High Order Fluid-Structure Interaction Solver

Lectures on the Orbital Stability of Standing Waves and Application to the Nonlinear Schrodinger Equation

Steady-state Solutions in Mathematical Models of Atrial Cell Electrophysiology and their Stability

Uncertainty analysis for the steady-state flows in a dual throat nozzle

Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity

A Globally Convergent Algorithm for the Run-to-Run Control of Systems with Sector Nonlinearities

Nonlinear quasisteady state benchmark of global gyrokinetic codes

Construction of a High Order Fluid-Structure Interaction Solver

Lectures on the Orbital Stability of Standing Waves and Application to the Nonlinear Schrodinger Equation

Steady-state Solutions in Mathematical Models of Atrial Cell Electrophysiology and their Stability

Uncertainty analysis for the steady-state flows in a dual throat nozzle

Analytical approximations for the collapse of an empty spherical bubble

The Bounded Confidence Model Of Opinion Dynamics

The Bounded Confidence Model Of Opinion Dynamics