1) Potential well method
位势井方法
1.
The initial boundary value problem for the damped singularly perturbed Boussinesq-type equation utt-uxx-αux4-βux6+but=σ(u)xx,x∈Ω,t>0,u(0,t)=u(1,t)=uxx(0,t)=uxx(1,t)=ux4(0,t)=ux4(1,t)=0,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,is studied by the potential well method,where uxi=iuxi,σ(s) is a given nonlinear function,α and β are two positive constants,b≥0 is a real number,and Ω=(0,1).
采用位势井方法研究一类具弱阻尼的奇性扰动Boussinesq型方程的初边值问题utt-uxx-αux4-βux6+but=σ(u)xx,x∈Ω,t>0,u(0,t)=u(1,t)=uxx(0,t)=uxx(1,t)=ux4(0,t)=ux4(1,t)=0,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,其中uxi=ixui,σ(s)是一个已知的非线性函数,α和β是两个正的实常数,b≥0是任意实数,Ω=(0,1)。
2) potential well
位势井
1.
First,the potential well W and a family of potential wells are defined.
定义了位势井W及一族位势井,证明了若满足一定的条件,则此问题存在一个整体弱解,且此解在这族位势井中,最后证明了整体强解的存在唯一性。
2.
By introducing a family of potential wells we obtain a threshold result of global existence and nonexistcnce of solutions.
通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果。
3.
By using potential well family method,we study the invariant sets and vacuum isolating behaviour of solutions to a class of nonlinear wave equations.
应用位势井族方法,研究了一类非线性波动方程的不变集合与解的真空隔离,证明了当初始能量小于位势井深度时,此问题存在不变集合与解的真空隔离现象。
3) potential wells
位势井
1.
By using the theory of potential wells,it is shown that if f(u)satisfies assumption (H),u0(x)∈H10 (Ω),J(u0)=d and I(u0)<0,then the problem does not admit any global solution.
利用位势井族方法证明了:若f(u)满足假设(H),u0(x)∈H10(Ω),J(u0)=d且I(u0)<0,则此问题不存在整体解,这样就从根本上解决了这一公开问题,并从实质上补充了已有的结果。
2.
By using potential wells combined with the Galerkin method, it is shown that ifpsatisfies 1<p<∞,n=1,2;1<p≤n+2n-2,n≥3, u0(x)∈H1(Rn),0<E(0)<d,I(u)>0 or ‖u0‖=0, then the problem has the global solutions u(x,t):u∈W,0≤t<∞ and u∈L∞(0,∞;H1(Rn)),ut∈L∞(0,∞;L2(.
研究一类在非线性光学中提出的Schrdinger方程的Cauchy问题iut+Δu+|u|p-1u=0;u(x,0)=u0(x),x∈Rn,t≥0的整体解存在性问题,由于此时问题已不再具有正定能量,通过利用Galerkin结合位势井的方法证明了在满足条件10或‖u0‖=0时,问题存在整体解u(x,t):u∈W,0≤t<∞且u∈L∞(0,∞;H1(Rn)),ut∈L∞(0,∞;L2(Rn))。
3.
In this paper,we study the Cauchy problem of nonlinear Klein-Gordonequations By introducing a family of potential wells, we not only give a threshold resultof global existence and nonexistence of solutions, but also obtain the vacuumisolating of solutions.
本文研究了以下非线性K1ein-Gordon方程的柯西问题 通过引进一族位势井，不仅得到了该问题解的整体存在性与不存在的门槛结果，而且也得到了解的真空隔离现象。
4) 3-wells potential
三井位势
1.
By virtue of invariant manifolds and study of homoclinic and heteroclinic orbits,we described the structure of phase plane of JS model and gave enlighten global results on homoclinic and heteroclinic bifurcation in a Hamiltonian system with 3-wells potential.
研究一类带附加应力扩散项的Johnson-Segalman模型,通过不变流形分析方法以及同宿轨与异宿轨的研究,刻画了该模型的相空间结构,并证明了一类具有三井位势的Hamilton系统同宿轨和异宿轨的存在性。
5) potential wells
位势井族
1.
The existence of the weak solutions of the above problem is discussed by combining the Galerkin method and the family of new potential wells that defined in this paper, and the new existence terms are obtained.
首先，利用新定义的位势井族结合Galerkin方法对整体弱解的存在性进行研究，得到了新的弱解的存在条件。
2.
First by using new method we introduce a family of potential wells which include the single well as a special case.
首先我们应用新的方法引进了一族新的位势井，其中包括我们所熟知的位势井作为新位势井族的特例，然后应用这族新位势井得到了问题(1)-(3)的整体解的新的存在性定理及相关的推论，进而研究了问题(1)-(3)解的不变集合和解的真空隔离现象。
6) superiority trend
优势方位
补充资料：白银有色金属公司深部铜矿主井和副井
白银有色金属公司深部铜矿主井和副井
白银有色金属公司深部铜矿主井和副井
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条