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1.
A. I. Kozhanov 《Siberian Mathematical Journal》1994,35(5):945-956
Conclusion The results presented in § 1 and § 2 can serve as a basis for further study of equations like (1.1), (2.1)–(2.3). For example, using the obtained estimates for a solution u(x,t) together with the well-known estimates for solutions to the Cauchy problem or the maximum principle for parabolic equations [6, 7], we can easily obtain estimates for the derivativesu
t
(x, t),u
tt
(x, t), etc., as well as estimates for the derivatives with respect to the space variables.Concluding the article, we note that, in our opinion, together with the questions of existence and nonexistence of smooth solutions it is worthwhile to study some questions that concern qualitative properties of solutions to the considered equations, for example the questions of localization of solutions and some other questions.Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 35, No. 5, pp. 100–1005, September–October, 1994. 相似文献
2.
It is established that the linear problemu
u
–a
2
u
xx
=g(x,t),u(0,t) =u(x, t + T) =u(x,t) is always solvable in the function spaceA = {g:g(x,t) =g(x,t+T) =g( –x,t) = –g(–x,t)} provided thataTq = (2p – 1) and (2p – 1,q) = 1, wherepandq are integer numbers. To prove this statement, an exact solution is constructed in the form of an integral operator, which is used to prove the existence of a solution of a periodic boundary-value problem for a nonlinear second-order wave equation. The results obtained can be used when studying the solutions to nonlinear boundary-value problems by asymptotic methods.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1115–1121, August, 1993. 相似文献
3.
V. G. Romanov 《Mathematical Notes》1976,19(4):360-363
In this paper we consider an inverse problem for the differential equationu
t
=u
xx
+q(x, t) u; the problem amounts to finding the coefficient q(x, t) from the solution of a series of Cauchy problems for this equation, the solution being specified on some manifold. Our main result is a proof of a uniqueness theorem.Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 595–600, April, 1976. 相似文献
4.
T. E. Pyasetskaya 《Journal of Mathematical Sciences》1993,67(4):3225-3228
We consider the behavior of a solution of the wave equation utt (t, x) – a2 (t) uxx (t, x)=f (t, x) with initial conditions u (0, x)=u0, /t6t u (t, x) ¦t=0
=u1 (x), a andf being random functions; a(t) characteristizes the variable character of the medium;f(t, x) is the inhomogeneity, having the character of random walks.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 75–78, 1988. 相似文献
5.
Khoang Van Lai 《Ukrainian Mathematical Journal》1990,42(8):1006-1015
We construct an approximate solution for an initial boundary-value problem of the formu
t
(x, t) + a (x, t) ux
(x, t)=b (x, t, u), u (x, 0)=u0 (x),u (0,t)=u1 (t) by the method of characteristics. It is proved that the approximate solution converges to the exact one with rate of convergence of second order.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 8, pp. 1128–1138, August, 1990. 相似文献
6.
Shi Ronghua 《应用数学学报(英文版)》1985,2(2):154-160
In this paper we prove the following main results:
Theorem A. If bind (G)3/2, thenG–u has a Hamiltonian circuit for every vertexu of graphG
i, unlessG belongs either to two classesH
1 andH
2 of graphs or to some smaller order graphs with |V(G)|17.
Theorem B. If bind (G)3/2 and the maximum degree (G)>(n–1)/2, |V(G)|=n>17, thenG is pancyclic (i.e., it contains a circuit of every lengthm, 3m|V(G)|). 相似文献
7.
In this paper we study initial value problems likeu
t–R¦u¦m+uq=0 in n× +, u(·,0+)=uo(·) in N, whereR > 0, 0 <q < 1,m 1, andu
o is a positive uniformly continuous function verifying –R¦u
o¦m+u
0
q
0 in
N
. We show the existence of the minimum nonnegative continuous viscosity solutionu, as well as the existence of the function t(·) defined byu(x, t) > 0 if 0<t<t
(x) andu(x, t)=0 ift t
(x). Regularity, extinction rate, and asymptotic behavior of t(x) are also studied. Moreover, form=1 we obtain the representation formulau(x, t)=max{([(u
o(x – t))1–q
–(1–q)t]+)1/(1–q): ¦¦R}, (x, t)
+
N+1
.Partially supported by the DGICYT No. 86/0405 project. 相似文献
8.
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
9.
Alfred Louis 《Numerische Mathematik》1979,33(1):43-53
Summary Letu
h
be the finite element solution to–u=f with zero boundary conditions in a convex polyhedral domain . Fromu
h
we calculate for eachz and ||1 an approximationu
h
–
(z) toD
u(z) with |D
u(z)–u
h
–
(z)|=O(h
2k–2) wherek is the order of the finite elements. The same superconvergence order estimates are obtained also for the boundary flux. We need not work on a regular mesh but we have to compute averages ofu
h
where the diameter of the domain of integration must not depend onh. 相似文献
10.
The system of differential relations that arises in connection with the Bullough-Dodd-Zhiber-Shabat equationu
xt=eu–e–2u is considered. The consistency of this system is established, and it is shown that the system realizes a Bäcklund autotransformation for the equationu
xt=eu–e–2u. The associated three-dimensional dynamical systems, which are compatible on a two-dimensional invariant submanifold, are investigated, and a construction of their general solution, which gives the explicit form of the three-parameter soliton for the equationu
xt=eu–e–2u, is proposed.Bashkir State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 146–159, April, 1993. 相似文献
11.
A. N. Vityuk 《Ukrainian Mathematical Journal》1995,47(4):617-621
The existence of a generalized solution with continuous derivativesu
x
,u
y
is proved for the differential inclusionu
xy
F(x, y, u) with a nonconvex right-hand side satisfying the Lipschitz conditioninx, y, andu.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 531–534, April, 1995. 相似文献
12.
The wave equation for Dunkl operators 总被引:1,自引:0,他引:1
Let k = (kα)αε, be a positive-real valued multiplicity function related to a root system , and Δk be the Dunkl-Laplacian operator. For (x, t) ε N, × , denote by uk(x, t) the solution to the deformed wave equation Δkuk,(x, t) = δttuk(x, t), where the initial data belong to the Schwartz space on N. We prove that for k 0 and N l, the wave equation satisfies a weak Huygens' principle, while a strict Huygens' principle holds if and only if (N − 3)/2 + Σαε+kα ε . Here + is a subsystem of positive roots. As a particular case, if the initial data are supported in a closed ball of radius R > 0 about the origin, the strict Huygens principle implies that the support of uk(x, t) is contained in the conical shell {(x, t), ε N × | |t| − R x |t| + R}. Our approach uses the representation theory of the group SL(2, ), and Paley-Wiener theory for the Dunkl transform. Also, we show that the (t-independent) energy functional of uk is, for large |t|, partitioned into equal potential and kinetic parts. 相似文献
13.
László Losonczi 《Aequationes Mathematicae》1994,47(2-3):203-222
Summary In this paper we find the general measurable solutions of the functional equationF(xy) + F(x(1 – y)) – F((1 – x)y) – F((1 – x)(1 – y)) = G(x)H(y) (x, y ]0, 1[) whereF, G, H:]0, 1[ C are unknown functions. The solution of this equation is part of our program to determine the measurable solutions of the functional equationF
11
(xy) + F
12
(x(1 – y)) + F
21
((1 – x)y) + F
22
((1 – x)(1 – y)) = G(x)H(y) (x, y ]0, 1[). Our method of solution is based on the structure theorem of sum form equations of (2, 2)-type and on a result of B. Ebanks and the author concerning the linear independence of certain functions. 相似文献
14.
A. Hernndez-Bastida M.P. Fernndez-Snchez E. Gmez-Dniz 《Insurance: Mathematics and Economics》2009,45(2):247-254
In Bayesian analysis it is usual to assume that the risk profiles Θ1 and Θ2 associated with the random variables “number of claims” and “amount of a single claim”, respectively, are independent. A few studies have addressed a model of this nature assuming some degree of dependence between the two random variables (and most of these studies include copulas). In this paper, we focus on the collective and Bayes net premiums for the aggregate amount of claims under a compound model assuming some degree of dependence between the random variables Θ1 and Θ2. The degree of dependence is modelled using the Sarmanov–Lee family of distributions [Sarmanov, O.V., 1966. Generalized normal correlation and two-dimensional Frechet classes. Doklady (Soviet Mathematics) 168, 596–599 and Ting-Lee, M.L., 1996. Properties and applications of the Sarmanov family of bivariate distributions. Communications Statistics: Theory and Methods 25 (6) 1207–1222], which allows us to study the impact of this assumption on the collective and Bayes net premiums. The results obtained show that a low degree of correlation produces Bayes premiums that are highly sensitive. 相似文献
15.
Fordyce A. Davidson Bryan P. Rynne 《Journal of Mathematical Analysis and Applications》2004,300(2):491-504
Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem (2) (4)
u(a)=u(b)=0,