共查询到20条相似文献,搜索用时 13 毫秒
1.
Luiz Gustavo Farah 《偏微分方程通讯》2013,38(1):52-73
We study the local well-posedness of the initial-value problem for the nonlinear “good” Boussinesq equation with data in Sobolev spaces H s for negative indices of s. 相似文献
2.
3.
Xu-Qian Fan 《manuscripta mathematica》2006,120(4):435-467
One of the main goals of this paper is to solve the Poincaré–Lelong equation on a class of Kähler manifolds with nonnegative holomorphic bisectional curvature, $\mathrm{Ric}(x)\geq \left(a\ln\ln\left(10+r(x)\right)\right)\Big/\big.\left(\left(1+r^2(x)\right)\ln(10+r(x))\right)One of the main goals of this paper is to solve the Poincaré–Lelong equation on a class of K?hler manifolds with nonnegative holomorphic bisectional curvature, for some a > 67(n + 4)2. We will also study the Poisson equation on complete noncompact manifolds which satisfy volume doubling and Poincaré inequality. 相似文献
4.
OntheSuitableWeakSolutionsfortheCauchyProblemoftheBoussinesqEquationsGuoBoling(郭柏灵),YuanGuangwei(袁光伟)(InstituteofAppliedPhgsi... 相似文献
5.
S. I. Pohozaev 《Journal of Mathematical Sciences》2013,190(1):147-156
This paper is devoted to the problem of existence of global solutions of the Korteweg–de Vries equation. For certain initial–boundary problems for the Korteweg–de Vries equation, we obtain necessary conditions of existence (in other words, sufficient conditions of nonexistence) of global solutions. 相似文献
6.
Sh. M. Nasibov 《Doklady Mathematics》2018,98(3):586-588
The solution of the Cauchy problem for a nonlinear Schrödinger evolution equation with certain initial data is proved to blow up in a finite time, which is estimated from above. Additionally, lower bounds for the blow-up rate are obtained in some norms. 相似文献
7.
Bao-quan Yuan 《应用数学学报(英文版)》2006,22(3):413-418
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let (u(x,t),b(x,t)) be smooth solutions in (0, T). It is shown that the solution (u(x, t), b(x, t)) can be extended beyond t = T if (u(x,t), b(x, t)) ∈ L^1 (0, T; BMO) or the vorticity (rot u(x, t), rot b(x, t)) ∈ L^1 (0, T; BMO) or the deformation (Def u(x, t), Def b(x, t)) ∈ L^1 (0, T; BMO). 相似文献
8.
Quasipatterns (two-dimensional patterns that are quasiperiodic in any spatial direction) remain one of the outstanding problems
of pattern formation. As with problems involving quasiperiodicity, there is a small divisor problem. In this paper, we consider
8-fold, 10-fold, 12-fold, and higher order quasipattern solutions of the Swift–Hohenberg equation. We prove that a formal
solution, given by a divergent series, may be used to build a smooth quasiperiodic function which is an approximate solution
of the pattern-forming partial differential equation (PDE) up to an exponentially small error. 相似文献
9.
10.
11.
We study persistent properties of solutions of the semi-linear Schrödinger equations in weighted spaces. 相似文献
12.
13.
V. Kostrykin K. A. Makarov A. K. Motovilov 《Integral Equations and Operator Theory》2005,51(1):121-140
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C. Under these assumptions we prove that the best possible value of the constant c in the condition
guaranteeing the existence of a (bounded) solution to the operator Riccati equation XA–CX+XBX = B* is equal to
We also prove an extension of the Davis-Kahan tan theorem and provide a sharp estimate for the norm of the solution to the Riccati equation. If C is bounded, we prove, in addition, that the solution X is a strict contraction if B satisfies the condition
and that this condition is optimal. 相似文献
14.
we study an initial-boundary-value problem for the "good" Boussinesq equation on the half line
{δt^2u-δx^2u+δx^4u+δx^2u^2=0,t〉0,x〉0.
u(0,t)=h1(t),δx^2u(0,t) =δth2(t),
u(x,0)=f(x),δtu(x,0)=δxh(x).
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data (f, h, h1, h2) belong to the product space
H^5(R^+)×H^s-1(R^+)×H^s/2+1/4(R^+)×H^s/2+1/4(R^+)
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered. 相似文献
{δt^2u-δx^2u+δx^4u+δx^2u^2=0,t〉0,x〉0.
u(0,t)=h1(t),δx^2u(0,t) =δth2(t),
u(x,0)=f(x),δtu(x,0)=δxh(x).
The existence and uniqueness of low reguality solution to the initial-boundary-value problem is proved when the initial-boundary data (f, h, h1, h2) belong to the product space
H^5(R^+)×H^s-1(R^+)×H^s/2+1/4(R^+)×H^s/2+1/4(R^+)
1 The analyticity of the solution mapping between the initial-boundary-data and the with 0 ≤ s 〈 1/2. solution space is also considered. 相似文献
15.
It is proved that, for some initial data, the solutions of the Cauchy problem for the cubic Schrödinger evolution equation blow up in finite time whose exact value is estimated from above. In addition, lower bounds for the blow-up rate of the solution in certain norms are obtained.
相似文献16.
Differential Equations - We consider a nonlinear Schrödinger equation arising in a number of physical problems. It is shown that when the real part is separated in this equation, there arises... 相似文献
17.
For any positive integer n,the famous Smarandache power function SP(n) is defined as the smallest positive integer m such that n|mm,where m and n have the same prime divisors.The main purpose of this paper is using the elementary methods to study the positive integer solutions of an equation involving the Smarandache power function SP(n) and obtain some interesting results.At the same time,we give an open problem about the related equation. 相似文献
18.
Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptoticstability of the zero solution of a certain fourth order functional differential equations.The resultgeneralizes the well known results. 相似文献
19.
OntheSuitableWeakSolutionstotheBoussinesqEquationsinaBoundedDomainGuoBoling(郭柏灵)YuanGuangwei(袁光伟)(InstituteofAppliedPhysicsan... 相似文献