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1.
An approach to inverse problems based on the boundary control theory is developed. The dynamic problem to recover a density
of an inhomogeneous string via its free endopoint oscillations generated by an instantaneous force source is proposed. The
problem is to determine the coefficient ρ(x)>0 in the equation ρ(x)utt(x, t)−uxx(x, t)=0(x, t>0) with the conditions u|<0=0, ux(0, t)=δ(t) by using a known function (response) u(0, t)=r(t) (t>0). The authors propose an algorithm based upon the approach
and demonstrate its numerical efficiency in the test problems including those for nonmonotone ρ(x)'s. Bibliography: 12 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 186, pp. 37–49, 1990.
Translated by T. N. Surkova. 相似文献
2.
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
3.
We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II1. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues
and eigenfunctions of the problems asm→−0.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999. 相似文献
4.
We investigate the linear periodic problem u
tt
−u
xx
=F(x, t), u(x+2π, t)=u(x, t+T)=u(x, t), ∈ ℝ2, and establish conditions for the existence of its classical solution in spaces that are subspaces of the Vejvoda-Shtedry
spaces.
Ternopol’ Pedagogical Institute, Ternopol’. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 302–308,
February, 1997. 相似文献
5.
V. T. Filippov 《Algebra and Logic》1996,35(2):120-128
Let Φ be an associative commutative ring with unity, 1/6 ∈ Φ, write A for a Mal’tsev algebra over Φ, suppose that on A, the
function h(y, z, t, x, x)=2[{yz, t, x}x+{yx, z, x}t], where {x, y, z}=(xy)z−(xz)y+2x(yz), is defined, and assume that H(A)
is a fully invariant ideal of A generated by the function h. The algebra A satisfying an identity h(y, z, x, x, x)=0 [h(y,
z, t, x, x)=0] is called a Mal’tsev h0-algebra (h-algebra). We prove that in any Mal’tsev h0-algebra, the inclusion H(A)·A2⊆Ann A holds withAnnA the annihilator of A. This means that any semiprime h0-algebra A is an h-algebra. Every prime h0-algebra A is a central simple algebra over the quotient field Λ of the center of its algebra of right multiplications, R(A),
and is either a 7-dimensional non-Lie algebra or a 3-dimensional Lie algebra over Λ.
Supported by RFFR grant No. 94-01-00381-a.
Translated fromAlgebra i Logika, Vol. 35, No. 2, pp. 214–227, March–April, 1996. 相似文献
6.
The object of this paper is to study the existence of a solution of the Cauchy problemu
t=Δum−up, u(x,0)=δ(x) and when a solution exists, to study its behaviour ast→0. 相似文献
7.
We study a periodic problem for the equation u
tt−uxx=g(x, t), u(x, t+T)=u(x, t), u(x+ω, t)= =u(x, t), ℝ2 and establish conditions of the existence and uniqueness of the classical solution.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 558–565, April, 1997. 相似文献
8.
We consider the existence and uniqueness of singular solutions for equations of the formu
1=div(|Du|p−2
Du)-φu), with initial datau(x, 0)=0 forx⇑0. The function ϕ is a nondecreasing real function such that ϕ(0)=0 andp>2.
Under a growth condition on ϕ(u) asu→∞, (H1), we prove that for everyc>0 there exists a singular solution such thatu(x, t)→cδ(x) ast→0. This solution is unique and is called a fundamental solution. Under additional conditions, (H2) and (H3), we show the
existence of very singular solutions, i.e. singular solutions such that ∫|x|≤r
u(x,t)dx→∞ ast→0. Finally, for functions ϕ which behave like a power for largeu we prove that the very singular solution is unique. This is our main result.
In the case ϕ(u)=u
q, 1≤q, there are fundamental solutions forq<p*=p-1+(p/N) and very singular solutions forp-1<q<p*. These ranges are optimal.
Dedicated to Professor Shmuel Agmon 相似文献
9.
Pedro E. Ferreira 《Annals of the Institute of Statistical Mathematics》1982,34(1):423-431
Summary Let {p(x, θ): θ∈Θ} be a family of densities where θ=(θ1,θ2), being θ1 ∈ Θ1 ak-dimensional parameter of interest, θ2 ∈ Θ2 a nuisance parameter and Θ=Θ1×Θ2. To estimate θ1, vector estimating equations g(x,θ1)=(g1(x,θ1),...,gk(x,θ1))=0 are considered. The standardized form of g(x,θ1) is defined as gs=(Eθ(∂g/∂θ′1))−1g. Then, within the classG
1 of unbiased equations (i.e. satisfying Eθ(g)=0 (θ∈Θ)), an equationg
*=0 is said to be optimum if the covariance matrices ofg
s andg
s
*
are such that
is non-negative definite for allg∈
G
1 and θ∈Θ. Sufficient conditions for optimality are discussed and, in particular, conditions for the optimality of the maximum
conditional likelihood equation are analyzed. Special attention is given to non-regular cases. In addition, measures of the
information about θ1 contained in an estimating equation are presented and a Rao-Blackwell theorem is given.
CIENES 相似文献
10.
M. N. Yakovlev 《Journal of Mathematical Sciences》2000,101(4):3361-3364
The solvability conditions for the equation Tu+F(u)=0 are found in the case where the operator [T+F′(u)]−1 exists only for u∈K, where K is a cone in a Banach space X. An application concerning the solvability of boundary-value problems
for systems of second-order differential equations is provided.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 225–230.
Translated by L. Yu. Kolotilina. 相似文献
11.
V. E. Slyusarchuk 《Ukrainian Mathematical Journal》1997,49(7):1089-1101
We establish conditions of asymptotic stability for all solutions of the equation X
n+1=F(X
n
), n≥0, in the Banach space E in the case where r(F′(x))<1 ∀ x ∈ E, r′(x) is the spectral radius of F′(x). An example of an equation with an unstable solution is given.
Ukrainian Academy of the Water Industry, Rovno. Translated from Ukrainskii Matematicheskii zhurnal, Vol. 49, No. 7, pp. 970–980.
July, 1997. 相似文献
12.
V. A. Kondratiev 《Journal of Mathematical Sciences》2006,135(1):2666-2674
The equations under consideration have the following structure:
where 0 < x
n < ∞, (x
1, …, x
n−1) ∈ Ω, Ω is a bounded Lipschitz domain,
is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations
as x
n → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas
were obtained in the case of a
ij, ai depending only on (x
1, …, x
n−1).
__________
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 98–111, 2005. 相似文献
13.
M. M. Gekhtman 《Mathematical Notes》1977,21(2):117-118
Let A>0 be an unbounded self-adjoint operator in a Hilbert space H. In the Hilbert space H1=L2 (0, π; H) we study the spectrum of the differential equations−y″(x)+Ay=λy, y (0)=y(π)=0,−y″(x)+Ay=λy, y′(0) =y′(π)=0. We find the principal terms of the asymptotics of the functions N(λ) for these problems and we ascertain the conditions
under which they are asymptotically not equivalent.
Translated from Matematicheskie Zametki, Vol. 21, No. 2, pp. 209–212, February, 1977. 相似文献
14.
V. A. Bykovskii 《Functional Analysis and Its Applications》2000,34(2):98-105
The Dirichlet (Hecke-Maass) series associated with the eigenfuctionsf andg of the invariant differential operator Δk=−y2(∂2/∂x2)+iky∂/∂x of weightk are investigated. It is proved that any relation of the form (f/kM)=g for thek-action of the groupSL
2
SL
2(ℝ) is equivalent to a pair of functional equations relating the Hecke-Maass series forf andg and involving only traditional gamma factors.
This work was supported by the Russian Foundation for Basic Research (grant No. 96-01-10439).
Institute of Applied Mathematics, Far East Division of Russian Academy of Sciences. Translated from Funktional'nyi Analiz
i Ego Prilozheniya, Vol. 34, No. 2, pp. 23–32, April–June, 2000.
Translated by V. M. Volosov 相似文献
15.
This paper gives conditions ensuring the existence for an initial value (x
0,v
0) of a solution to the second order differential inclusionx″(t) ∈F[x(t),x′(t)],x(0)=x
0,x′(0)=v
0 such thatx(t) ∈K for allt whereK is a nonempty given subset ofR
n
.
相似文献
16.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
17.
V. T. Filippov 《Algebra and Logic》1997,36(3):193-203
Let ϕ be an associative commutative ring with 1, containing 1/6, and A be an alternative ϕ-algebra. Let D be an associator
ideal of A and H a fully invariant ideal of A, generated by all elements of the form h(y, z, t, x, x)=[{[y, z], t, x}-, x]+[{[y,
x], z, x}-, t], where [x, y]=xy−yx, {x, y, z}-=[[x, y], z]−[[x, z], y]+2[x,[y, z]]. Here we consider an ideal Q=H∩D and prove
that Q4=0 in the algebra A. If A is unmixed, then HD=0, DH=0, and Q2=0 in particular. If A is a finitely generated unmixed algebra, then the ideal H lies in its associative center and Q=0. It
follows that any finitely generated purely alternative algebra satisfies the identity h(y,z,t,x,x)=0. We also show that a
fully invariant ideal H0 of the unmixed algebra A, generated by all elements of the form h(x, z, t, x, x), lies in its associative center and H0∩D=0. Consequently, every purely alternative algebra satisfies the identity h(x,z,t,x,x)=0.
Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 323–340, May–June, 1997. 相似文献
18.
Manabu Naito 《Annali di Matematica Pura ed Applicata》2007,186(1):59-84
In this paper the even-order quasilinear ordinary differential equation
is considered under the hypotheses that n is even, D(α
i
)x = (|x|αi−1 x)′, α
i
> 0(i = 1,2,…, n), β > 0, and p(t) is a continuous, nonnegative, and eventually nontrivial function on an infinite interval [a, ∞), a > 0. The existence of positive solutions of (1.1) is discussed, and basic results to the classical equation
are extended to the more general equation (1.1). In particular, necessary and sufficient integral conditions for the existence
of positive solutions of (1.1) are established in the case α 1α2⋅s α
n
≠ β.
This research was partially supported by Grant-in-Aid for Scientific Research (No. 15340048), Japan Society for the Promotion
of Science.
Mathematics Subject Classification (2000) 34C10, 34C11 相似文献
19.
The collocation method by spline in tension for the problem: −εy"+p(x)y=f(x), y(0)=α0,y(1)=α1, p(x)>0, 0<ε<<1, is derived. The method has the second order of the global uniform convergence. For the corresponding difference
scheme the optimal estimate: O (himin(hi, ε) is obtained.
This research was supported partly by NSF and SIZ for Science of SAP Vojvodina through funds made available to the U.S.—Yugoalav
Joint Board on Scientific and Tchnological Cooperation (grants JF554, JF799). 相似文献
20.
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