Results 21 to 30 of about 11,284,175 (207)

Construction of Hadamard states by characteristic Cauchy problem [PDF]

, 2014
We construct Hadamard states for Klein-Gordon fields in a spacetime $M_{0}$ equal to the interior of the future lightcone $C$ from a base point $p$ in a globally hyperbolic spacetime $(M, g)$.
C. G'erard, M. Wrochna
semanticscholar   +1 more source

The affine Cauchy problem

Journal of Mathematical Analysis and Applications, 2009
AbstractThe aim of this paper is to solve the Cauchy problem for locally strongly convex surfaces which are extremal for the equiaffine area functional. These surfaces are called affine maximal surfaces and here, we give a new complex representation which let us describe the solution to the corresponding Cauchy problem.
Antonio Martínez, Juan A. Aledo, Francisco Milán   +2 more
openaire   +2 more sources

On the Cauchy problem for the Schrödinger-Hartree equation

, 2015
In this paper, we undertake a comprehensive study for the Schrodinger-Hartree equation \begin{equation*} iu_t +\Delta u+ \lambda (I_\alpha \ast |u|^{p})|u|^{p-2}u=0, \end{equation*} where $I_\alpha$ is the Riesz potential.
Binhua Feng, Xian-Zhi Yuan
semanticscholar   +1 more source

Cauchy problem for fractional diffusion-wave equations with variable coefficients [PDF]

, 2013
We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables.
A. Kochubei
semanticscholar   +1 more source

On the nonlocal Cauchy problem for semilinear fractional order evolution equations

, 2014
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam.
Jinrong Wang, Yong Zhou, Michal Feckan
semanticscholar   +1 more source

On the Cauchy Problem for the Zakharov System

Journal of Functional Analysis, 1997
The authors study the local Cauchy problem in time for the Zakharov system in arbitrary space dimension \(D\). It is used a contraction or fixed point method, which is a simpler version than that used by Bourgain. A basic tool is the extension to the Zakharov system the notion of criticality which applies to dilation covariant equations as the ...
Giorgio Velo, J. Ginibre, Y. Tsutsumi
openaire   +4 more sources

Cauchy Problem with Subcritical Nonlinearity

Journal of Mathematical Analysis and Applications, 1997
The authors consider the asymptotic behaviour of solutions of parabolic systems \[ u_t=- Au+f(u_1,\dots,u_d,\dots, \partial^\alpha_iu_j,\dots),\;i\leq n,\;j\leq d,\;(x,t)\in\mathbb{R}^n\times \mathbb{R}_+,\tag{1} \] with \(u(0,x)= u_0(x)\). In (1), \(A\) is a linear matrix operator of uniformly elliptic type of order \(2m\) while the order \(\alpha ...
Jan W. Cholewa, Tomasz Dlotko
openaire   +3 more sources

On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order. [PDF]

Entropy (Basel), 2022
Juraev DA, Shokri A, Marian D.
europepmc   +1 more source

Local Well-Posedness to the Cauchy Problem for an Equation of the Nagumo Type. [PDF]

ScientificWorldJournal, 2022
Lizarazo V, De la Cruz R, Lizarazo J.
europepmc   +1 more source

The Cauchy process and the Steklov problem

Journal of Functional Analysis, 2004
Given the Cauchy process \((X_{t})\) on \(\mathbb R^d\), \(d\geq 1\), the authors investigate the spectral properties of the semigroup \((P_{t}^D)\) obtained from \((X_{t})\) by killing the process upon leaving the bounded open set \(D\) whose boundary has to satisfy some (Lipschitz) regularity property.
Tadeusz Kulczycki, Tadeusz Kulczycki, Rodrigo Bañuelos   +2 more
openaire   +3 more sources