1) potential well
势井
1.
The Galerkin method,together with the potential well(stable set) method,is employed to solve the existence of global weak solutions of the primary limit value of a kind of semi-linear parabolic equations: in case of high dimension when.
运用Galerkin方法并结合势井理论,证明了一类半线性抛物型方程ut-Δu+up=0的高维情形的初边值混和问题在t 0的整体弱解的存在性。
2.
According to the potential well theory, by constructing unstable set and using the revised convexity method, the blow up property of the solution for the mixed problem of some nonlinear wave equations uuuutt1||-=D-gwas proved in a simple way.
依据势井理论,通过构造不稳定集,应用经过改进的凸性分析方法,简单明了地证明了一类非线性波动方程uuuutt1||-=D-g的混合问题解的爆破性质,即当初值属于不稳定集,初始能量为正但有适当上界时,解在L2范数意义下在有限时刻发生爆破。
3.
In this paper, we study the existence of solutions for wave equations with two nonlinear source terms of different signs: utt-△u+a|u|p-1u-b|u|q-1u=0 by theory of potential wells and Galerkin method.
依据势井理论,引入了一簇势井,并结合紧致性方法得到该问题整体解的存在性。
2) acoustic potential well
声势井
3) 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。
4) 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。
5) 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。
6) 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。
补充资料：村村势势
1.犹言土头土脑。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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