Results 1 to 10 of about 9,689,661 (201)

On the well-posedness of the vacuum Einstein’s equations [PDF]

Journal of Evolution Equations, 2011
33 ...
openaire   +3 more sources

On the Well-posedness of Bayesian Inverse Problems [PDF]

SIAM/ASA Journal on Uncertainty Quantification, 2020
30 pages, 7 ...
openaire   +3 more sources

Stability of energy-critical nonlinear Schrodinger equations in high dimensions

Electronic Journal of Differential Equations, 2005
We develop the existence, uniqueness, continuity, stability, and scattering theory for energy-critical nonlinear Schrodinger equations in dimensions $n geq 3$, for solutions which have large, but finite, energy and large, but finite, Strichartz norms ...
Terence Tao, Monica Visan
doaj  

Well-posedness of stochastic modified Kawahara equation

Advances in Difference Equations, 2020
In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in Hs(R) $H^{s}(\mathbb{R})$, s≥−1/4 $s\geq -1/4$. Moreover, we get the
P. Agarwal, Abd-Allah Hyder, M. Zakarya
doaj   +1 more source

Remark on well-posedness and ill-posedness for the KdV equation

Electronic Journal of Differential Equations, 2010
We consider the Cauchy problem for the KdV equation with low regularity initial data given in the space $H^{s,a}(mathbb{R})$, which is defined by the norm $$ | varphi |_{H^{s,a}}=| langle xi angle^{s-a} |xi|^a widehat{varphi} |_{L_{xi}^2}.
Takamori Kato
doaj  

AN INTRODUCTION TO WELL-POSEDNESS AND FREE-EVOLUTION [PDF]

International Journal of Modern Physics A, 2013
These lecture notes accompany two classes given at the NRHEP2 school. In the first lecture I introduce the basic concepts used for analyzing well-posedness, that is the existence of a unique solution depending continuously on given data, of evolution partial differential equations.
openaire   +3 more sources

Well-Posedness of MultiCriteria Network Equilibrium Problem

Abstract and Applied Analysis, 2014
New notions of ϵ-equilibrium flow and ξk0-ϵ-equilibrium flow of multicriteria network equilibrium problem are introduced; an equivalent relation between vector ϵ-equilibrium pattern flow and ξk0-ϵ-equilibrium flow is established. Then, the well-posedness
W. Y. Zhang
doaj   +1 more source

Well-Posedness of the Iterative Boltzmann Inversion [PDF]

Journal of Statistical Physics, 2017
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is reported to work reasonably well in practice, it still lacks a rigorous convergence analysis. In this paper we provide
openaire   +2 more sources

Well-Posedness by Perturbations of Generalized Mixed Variational Inequalities in Banach Spaces

Journal of Applied Mathematics, 2012
We consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi (1995, 1996) for a minimization problem, to a class of generalized mixed variational inequalities in Banach spaces, which includes as a special case the ...
Lu-Chuan Ceng, Ching-Feng Wen
doaj   +1 more source

Well-posedness and ill-posedness of the fifth-order modified KdV equation

Electronic Journal of Differential Equations, 2008
We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. $$displaylines{ partial_t u - partial_x^5u + c_1partial_x^3(u^3) + c_2upartial_x upartial_x^2 u + c_3uupartial_x^3 u =0cr u(x,0)= u_0(x ...
Soonsik Kwon
doaj