共查询到20条相似文献,搜索用时 15 毫秒
1.
I. V. Dombrovskii 《Ukrainian Mathematical Journal》1999,51(11):1779-1781
We establish conditions for the existence of a smooth solution of a quasilinear hyperbolic equationu
tt
- uxx = ƒ(x, t, u, u, u
x),u (0,t) = u (π,t) = 0,u (x, t+ T) = u (x, t), (x, t) ∈ [0, π] ×R, and prove a theorem on the existence and uniqueness of a solution.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1574–1576, November, 1999. 相似文献
2.
We study the boundary value problem for the quasilinear equation u u ? uxx=F[u, ut], u(x, 0)= u(x, π)=0, u(x+w, t)=u(x, t), x ε ®, t ε [0, π], and establish conditions under which a theorem on the uniqueness of a smooth solution is true. 相似文献
3.
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
4.
5.
N. G. Khoma 《Ukrainian Mathematical Journal》1995,47(12):1964-1967
We study a periodic boundary-value problem for the quasilinear equationu
tt–uxx=F[u, ut], u(0, t)=u(, t)=0,u(x, t+2)=u(x, t). We establish conditions that guarantee the validity of the uniqueness theorem.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1717–1719, December, 1995. 相似文献
6.
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
7.
8.
A. G. Botyuk 《Ukrainian Mathematical Journal》1997,49(12):1907-1911
We study a periodie boundary-value problem for the quasilinear equation u tt ? u xx = F[u, u t , u x ]. We find conditions under which a theorem on the uniqueness of a solution is true. 相似文献
9.
10.
In the space of functions B
a3+={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT
3
(2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u
u
−a
2
u
xx
=g(x, t), u(0, t)=u(π, t)=0, u(x, t+T
3
)=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator.
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308,
Feburary, 1997
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308,
Feburary, 1997 相似文献
11.
We consider a nonlocal boundary-value problem for the Poisson equation in a rectangular domain. Dirichlet conditions are posed on a pair of adjacent sides of a rectangle, and integral constraints are given instead of standard boundary conditions on the other pair. The corresponding difference scheme is constructed and investigated; an a priori estimate of the solution is obtained with the help of energy inequality method. Discretization error estimate that is compatible with the smoothness of the solution sought is obtained. 相似文献
12.
É. I. Abduragimov 《Mathematical Notes》2012,91(5-6):755-763
An iterative method is proposed for finding an approximation to the positive solution of the two-point boundary-value problem $y'' + c(x)y^m = 0,0 < x < 1,y(0) = y(1) = 0,$ where m = const > 1 and c(x) is a continuous nonnegative function on [0, 1]. The convergence of this method is proved. An error estimate is also obtained. 相似文献
13.
14.
15.
M. Sh. Shabozov 《Ukrainian Mathematical Journal》1998,50(8):1312-1317
We study the problem of renewal of a solution of the Dirichlet boundary-value problem for a biharmonic equation on the basis
of the known information about the boundary function. The obtained estimates of renewal error are unimprovable in certain
cases.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1147–1151, August, 1998. 相似文献
16.
We consider an approximate method for the solution of the Cauchy problem for an operator differential equation. This method
is based on the expansion of an exponential in orthogonal Laguerre polynomials. We prove that the fact that an initial value
belongs to a certain space of smooth elements of the operator A is equivalent to the convergence of a certain weighted sum of integral residuals. As a corollary, we obtain direct and inverse
theorems of the theory of approximation in the mean.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 557–563, April, 2008. 相似文献
17.
18.
G. Gaprindashvili 《Georgian Mathematical Journal》1995,2(1):21-36
The periodic boundary value problem for systems of secondorder ordinary nonlinear differential equations is considered. Sufficient conditions for the existence and uniqueness of a solution are established. 相似文献
19.
We study the boundary-value problemu
tt
-u
xx
=g(x, t),u(0,t) =u (π,t) = 0,u(x, t +T) =u(x, t), 0 ≤x ≤ π,t ∈ ℝ. We findexact classical solutions of this problem in three Vejvoda-Shtedry spaces, namely, in the classes of, and-periodic functions (q and s are natural numbers). We obtain the results only for sets of periods, and which characterize the classes of π-, 2π -, and 4π-periodic functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 281–284, February, 1999. 相似文献
20.
Ukrainian Mathematical Journal - 相似文献