Results 11 to 20 of about 264 (23)

The low regularity global solutions for the critical generalized KdV equation [PDF]

, 2009
We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces $H^s(\R)$ for $s>6/13$. Of course, we require that the mass is strictly less than that of the ground state in the focusing case.
Miao, Changxing, Shao, Shuanglin, Wu, Yifei, Xu, Guixiang   +3 more
core   +1 more source

Delayed loss of stability in singularly perturbed finite-dimensional gradient flows

, 2017
In this paper we study the singular vanishing-viscosity limit of a gradient flow in a finite dimensional Hilbert space, focusing on the so-called delayed loss of stability of stationary solutions.
Scilla, Giovanni, Solombrino, Francesco
core   +2 more sources

Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces [PDF]

, 2010
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$
Ramm, A. G.
core   +7 more sources

Well-posedness and stability results for the Gardner equation

, 2011
In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation.
C. Kenig, C. Kenig, C. Kenig, F. Linares, J. Angulo, J. Angulo, J. Colliander, M. Christ, M.I. Weinstein, Miguel A. Alejo, T. Tao   +10 more
core   +1 more source

Asymptotic stability of solutions to abstract differential equations [PDF]

, 2010
An evolution problem for abstract differential equations is studied. The typical problem is: $$\dot{u}=A(t)u+F(t,u), \quad t\geq 0; \,\, u(0)=u_0;\quad \dot{u}=\frac {du}{dt}\qquad (*)$$ Here $A(t)$ is a linear bounded operator in a Hilbert space $H ...
Ramm, A. G.
core   +4 more sources

Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data

, 2017
The aim of this note is to adapt the strategy in [4][See,B.Dodson, J.Murphy, a new proof of scattering below the ground state for the 3D radial focusing cubic NLS, arXiv:1611.04195 ] to prove the scattering of radial solutions below sharp threshold for ...
Sun, Chenmin, Wang, Hua, Yao, Xiaohua, Zheng, Jiqiang   +3 more
core   +1 more source

Dynamical systems and forward-backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator

, 2014
In a Hilbert framework, we introduce continuous and discrete dynamical systems which aim at solving inclusions governed by structured monotone operators $A=\partial\Phi+B$, where $\partial\Phi$ is the subdifferential of a convex lower semicontinuous ...
Abbas, Boushra, Attouch, Hedy
core   +1 more source

A nonlinear inequality and evolution problems [PDF]

, 2010
Assume that $g(t)\geq 0$, and $$\dot{g}(t)\leq -\gamma(t)g(t)+\alpha(t,g(t))+\beta(t),\ t\geq 0;\quad g(0)=g_0;\quad \dot{g}:=\frac{dg}{dt}, $$ on any interval $[0,T)$ on which $g$ exists and has bounded derivative from the right, $\dot{g}(t):=\lim_{s ...
Ramm, A. G.
core   +3 more sources

Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations

, 2014
In the paper we consider the problem of the rigorous description of the kinetic evolution in the presence of initial correlations of quantum large particle systems.
Gerasimenko, V. I.
core   +3 more sources

Towards Rigorous Derivation of Quantum Kinetic Equations

, 2010
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator.
Arnold A, Benedetto D, Bogolybov N N, Bogolybov N N, Bogolyubov M M, Bogolyubov N N, Borgioli G, Borgioli G, Bratelli O, Cercignani C, Cercignani C, Cohen E G D, Cohen E G D, Dautray R, Gerasimenko V I, Gerasimenko V I, Gerasimenko V I, Gerasimenko V I, Gerasimenko V I, Gerasimenko V I, Ginibre J, Grad H, Kato T, Petrina D Ya, Polishchuk D O, Spohn H, Spohn H, Tsvir Zh A, Uhlenbeck G E, V I Gerasimenko, Zh A Tsvir   +30 more
core   +1 more source