共查询到20条相似文献,搜索用时 31 毫秒
1.
N. G. Khoma 《Ukrainian Mathematical Journal》1998,50(11):1755-1764
In three spaces, we obtain exact classical solutions of the boundary-value periodic problem u
tt−a
2
u
xx=g(x,t), u(0,t)=u(π,t)=0, u(x,t+T)=u(x,t)=0, x,t∈ĝ
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1537–1544, November, 1998. 相似文献
2.
A. O. Botyuk 《Ukrainian Mathematical Journal》1997,49(7):1120-1124
We study the boundary-value perlodic problem u
tt
−u
xx
=F(x, t), u(0, t)=u(π, t)=0, u(x, t+T)=u(x, t), (x, t) ∈ R
2. By using the Vejvoda-Shtedry operator, we determine a solution of this problem.
Ternopol Pedagogical Institute, Temopol. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 7, pp. 998–1001,
July, 1997. 相似文献
3.
Maria E. Schonbek 《Mathematische Annalen》2006,336(3):505-538
This paper considers the existence and large time behavior of solutions to the convection-diffusion equation u
t
−Δu+b(x)·∇(u|u|
q
−1)=f(x, t) in ℝ
n
×[0,∞), where f(x, t) is slowly decaying and q≥1+1/n (or in some particular cases q≥1). The initial condition u
0 is supposed to be in an appropriate L
p
space. Uniform and nonuniform decay of the solutions will be established depending on the data and the forcing term.This work is partially supported by an AMO Grant 相似文献
4.
Zheng Zukang 《高校应用数学学报(英文版)》2004,19(1):90-100
An algorithm of continuous stage-space MCMC method for solving algebra equation f(x)=0 is given. It is available for the case that the sign of f(x) changes frequently or the derivative f′(x) does not exist in the neighborhood of the root, while the Newton method is hard to work. Let n be the number of random variables created by computer in our algorithm. Then after m=O(n) transactions from the initial value x
0,x* can be got such that |f(x*)|<e
−cm |f(x
0)| by choosing suitable positive constant c. An illustration is also given with the discussion of convergence by adjusting the parameters in the algorithm.
Supported by the National Natural Science Foundation of China (70171008). 相似文献
5.
Mi-na Jiang~ Yan-ling Xu~ Laboratory of Nonlinear Analysis Department of Mathematics Central China Normal University Wuhan China Department of Information Computer Science College of Science Huazhong Agriculture University Wuhan China 《应用数学学报(英文版)》2005,21(1):31-42
We investigate the asymptotic behavior of solutions of the initial-boundary value problem for the generalized BBM-Burgers equation u_t f(u)_x=u_(xx) u_(xx) on the half line with the conditions u(0, t)=, u-, u(∞,t)=u_ and, u_-相似文献
6.
Li Changpin 《应用数学学报(英文版)》2001,17(2):191-199
In this paper, we investigate the bifurcations of one class of steady-state reaction-diffusion equations of the formu″ + μu − u
k=0, subjectu(0)=u(π)=0, where μ is a parameter, 4≤kεZ
+. Using the singularity theory based on the Liapunov-Schmidt reduction, some satisfactory results are obtained.
This work is supported by the National Natural Science Foundation of China (No.19971057) and the Youth Science Foundation
of Shanghai Municipal Commission of Education (No.99QA66). 相似文献
7.
P. V. Tsynaiko 《Ukrainian Mathematical Journal》1998,50(9):1478-1482
We study a periodic boundary-value problem for the quasilinear equation u
tt
−u
xx
=F[u, u
t
, u
x
], u(x, 0)=u(x, π)=0, u(x + ω, t) = u(x, t), x ∈ ℝ t ∈ [0, π], and establish conditions that guarantee the validity of a theorem on unique solvability.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1293–1296, September, 1998. 相似文献
8.
《Applied Mathematics Letters》2002,15(6):727-734
This paper is concerned with the asymptotic behaviors of the solutions to the initial-boundary value problem for scalar viscous conservations laws ut + f(u)x = uxx on [0, 1], with the boundary condition u(0, t) = u−(t) → u−, u(1, t) = u+(t) → u+, as t → +∞ and the initial data u(x,0) = u0(x) satisfying u0(0) = u−(0), u0(1) = u+(1), where u± are given constants, u− ≠ u+ and f is a given function satisfying f″(u) > 0 for u under consideration. By means of an elementary energy estimates method, both the global existence and the asymptotic behavior are obtained. When u− 〈 u+, which corresponds to rarefaction waves in inviscid conservation laws, no smallness conditions are needed. While for u− > u+, which corresponds to shock waves in inviscid conservation laws, it is established for weak shock waves, that is, |u−−u+| is small. Moreover, when u±(t) ≡ u±, t ≥ 0, exponential decay rates are both obtained. 相似文献
9.
Zhu Ning 《高校应用数学学报(英文版)》1998,13(3):241-250
ANOTEONTHEBEHAVIOROFBLOW┐UPSOLUTIONSFORONE┐PHASESTEFANPROBLEMSZHUNINGAbstract.Inthispaper,thefolowingone-phaseStefanproblemis... 相似文献
10.
We consider the following singularly perturbed boundary-value problem:
on the interval 0 ≤x ≤ 1. We study the existence and uniqueness of its solutionu(x, ε) having the following properties:u(x, ε) →u
0(x) asε → 0 uniformly inx ε [0, 1], whereu
0(x) εC
∞ [0, 1] is a solution of the degenerate equationf(x, u, u′)=0; there exists a pointx
0 ε (0, 1) such thata(x
0)=0,a′(x
0) > 0,a(x) < 0 for 0 ≤x <x
0, anda(x) > 0 forx
0 <x ≤ 1, wherea(x)=f′
v(x,u
0(x),u′
0(x)).
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 520–524, April, 2000. 相似文献
11.
We study the sublinear elliptic equation, −Δ u = |u|psgn u + f(x,u) in the bounded domain Ω under the zero Dirichlet boundary condition. We suppose that 0 < p < 1 and |f(x,u)| is small enough near u = 0 and do not suppose that f(x,u) is odd on u. Then we prove that this problem has infinitely many solutions.
Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 16540179), Ministry of Education, Culture, Sports,
Science and Technology. 相似文献
12.
Y. Mammeri 《Acta Appl Math》2012,117(1):1-13
We study the periodic solution of a perturbed regularized Boussinesq system (Bona et al., J. Nonlinear Sci. 12:283–318, 2002, Bona et al., Nonlinearity 17:925–952, 2004), namely the system η
t
+u
x
+β(−η
xxt
+u
xxx
)+α((ηu)
x
+ηη
x
+uu
x
)=0,u
t
+η
x
+β(η
xxx
−u
xxt
)+α((ηu)
x
+ηη
x
+uu
x
)=0, with 0<α,β≤1. We prove that the solution, starting from an initial datum of size ε, remains smaller than ε for a time scale of order (ε
−1
α
−1
β)2, whereas the natural time is of order ε
−1
α
−1
β. 相似文献
13.
We study the large time behaviour of nonnegative solutions of the Cauchy problemu
t=Δu
m −u
p,u(x, 0)=φ(x). Specifically we study the influence of the rate of decay ofφ(x) for large |x|, and the competition between the diffusion and the absorption term. 相似文献
14.
Emilien Tarquini 《Monatshefte für Mathematik》2007,151(4):333-339
In this paper we consider the Gross-Pitaevskii equation iu
t
= Δu + u(1 − |u|2), where u is a complex-valued function defined on
, N ≥ 2, and in particular the travelling waves, i.e., the solutions of the form u(x, t) = ν(x
1 − ct, x
2, …, x
N
), where
is the speed. We prove for c fixed the existence of a lower bound on the energy of any non-constant travelling wave. This bound provides a non-existence
result for non-constant travelling waves of fixed speed having small energy. 相似文献
15.
In this paper, we are concerned with the global singularity structures of weak solutions to 4-D semilinear dispersive wave
equations whose initial data are chosen to be discontinuous on the unit sphere. Combining Strichartz's inequality with the
commutator argument techniques, we show that the weak solutions are C2−regular away from the focusing cone surface |x|=|t−1| and the outgoing cone surface |x|=t+1.
This research was supported by the National Natural Science Foundation of China and the Doctoral Foundation of NEM of China. 相似文献
16.
N. A. Chalkina 《Moscow University Mathematics Bulletin》2011,66(6):231-234
Sufficient conditions for the existence of an inertial manifold are found for the equation u
tt
+ 2γu
t
− Δu = f(u, u
t
), u = u(x, t), x ∈ Ω ⋐ ℝ
N
, u|
∂Ω = 0, t > 0 under the assumption that the function f satisfies the Lipschitz condition. 相似文献
17.
For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. 相似文献
18.
Emilien Tarquini 《Monatshefte für Mathematik》2007,243(1):333-339
In this paper we consider the Gross-Pitaevskii equation iu
t
= Δu + u(1 − |u|2), where u is a complex-valued function defined on
\Bbb RN×\Bbb R{\Bbb R}^N\times{\Bbb R}
, N ≥ 2, and in particular the travelling waves, i.e., the solutions of the form u(x, t) = ν(x
1 − ct, x
2, …, x
N
), where
c ? \Bbb Rc\in{\Bbb R}
is the speed. We prove for c fixed the existence of a lower bound on the energy of any non-constant travelling wave. This bound provides a non-existence
result for non-constant travelling waves of fixed speed having small energy. 相似文献
19.
S. G. Khoma 《Ukrainian Mathematical Journal》2000,52(4):655-657
We find conditions for the existence of the classical solution of the boundary-value problem u
tt
-u
xx
= f(x,t), u(0,t)=u(π, t)=0, u(x, 0)=u(x, 2π). 相似文献
20.
Let X be a Banach space, A : D(A) X → X the generator of a compact C0- semigroup S(t) : X → X, t ≥ 0, D a locally closed subset in X, and f : (a, b) × X →X a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order to make D a viable domain of the semilinear differential equation of retarded type u'(t) = Au(t) + f(t, u(t - q)), t ∈ [to, to + T], with initial condition uto = φ ∈C([-q, 0]; X), is the tangency condition lim infh10 h^-1d(S(h)v(O)+hf(t, v(-q)); D) = 0 for almost every t ∈ (a, b) and every v ∈ C([-q, 0]; X) with v(0), v(-q)∈ D. 相似文献