共查询到20条相似文献,搜索用时 9 毫秒
1.
L. S. Pul'kina 《Mathematical Notes》1992,51(3):286-290
Translated from Matematicheskie Zametki, Vol. 51, No. 3, pp. 91–96, March, 1992. 相似文献
2.
We consider a nonlocal problem for a degenerate equation in a domain bounded by characteristics of this equation. The boundary-value conditions of the problem include linear combination of operators of fractional integro-differentiation in the Riemann–Liouville sense. The uniqueness of solution of the problem under consideration is proved by means of the modified Tricomi method, and existence is reduced to solvability of either singular integral equation with the Cauchy kernel or Fredholm integral equation of second kind. 相似文献
3.
Said Mesloub 《Mathematical Methods in the Applied Sciences》2010,33(1):57-70
In this paper, we study a nonlocal mixed problem for a nonlinear hyperbolic equation. Based on some a priori estimates and some density arguments, we prove the well posedness of the associated linear problem. The existence and uniqueness of the weak solution of the nonlinear problem are then established by applying an iterative process based on the obtained results for the linear problem. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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In the characteristic triangle for a hyperbolic equation of the second kind we study a nonlocal problem, where the boundary value condition contains a linear combination of Riemann–Liouville fractional integro-differentiation operators. We establish variation intervals of orders of fractional integro-differentiation operators, taking into account parameters of the considered equation with which the mentioned problem has either a unique solution or more than one solution. 相似文献
6.
Z. A. Nakhusheva 《Differential Equations》2011,47(10):1468-1481
We find necessary and sufficient conditions for the unique solvability of the generalized Darboux problem for a degenerating
second-order linear hyperbolic equation of the first kind with two independent variables and with a spectral parameter. 相似文献
7.
Yu. A. Mitropol'skii M. Kh. Shkhanukov A. A. Berezovskii 《Ukrainian Mathematical Journal》1995,47(6):911-923
We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW
2
1,0
(Q
T
), and construct a difference scheme for the second-order approximation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 790–800, June, 1995. 相似文献
8.
In this paper we consider a boundary-value problem for one-dimensional hyperbolic equation with nonlocal initial data in integral form. We prove the existence and uniqueness of the generalized solution. 相似文献
9.
V. V. Tikhomirov 《Computational Mathematics and Modeling》2007,18(4):385-396
The spectral method is applied to establish solvability in the class of finite-energy generalized solutions of the mixed problem
for a hyperbolic equation with a nonlocal boundary condition of the first kind. The solution is representable as a biorthogonal
series in the root functions of the corresponding spectral problem.
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Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 167–178, 2004. 相似文献
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L. S. Pul’kina 《Differential Equations》2008,44(8):1119-1125
We consider a mixed initial-boundary value problem for a multidimensional (with respect to the space variables) hyperbolic equation with a nonlocal boundary condition containing an integral of the desired solution. We prove the unique solvability of the problem in the space W 2 1 . 相似文献
12.
For an equation of mixed type in a rectangular domain, we use spectral analysis to establish a uniqueness criterion for the solution of a problem with a nonlocal condition relating the values of the unknown solution that belong to different types of the considered equation. We prove the stability of the solution with respect to the nonlocal condition. 相似文献
13.
The initial boundary-value problem for the nonlinear nonlocal Sobolev equation is studied. Sufficient conditions for local and for global (with respect to time) solvability are obtained. For the case of local (not global) solvability, upper and lower bounds for the lifespan of the solution are obtained in the form of explicit and implicit formulas. 相似文献
14.
A. M. Denisov 《Proceedings of the Steklov Institute of Mathematics》2013,282(1):80-89
We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable Xe X has zero mean, we find the asymptotics of the survival probability at time n as n → ∞. 相似文献
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D. K. Durdiev 《Siberian Mathematical Journal》1992,33(3):427-433
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 69–77, May–June, 1992. 相似文献
17.
M. Kh. Beshtokov 《Computational Mathematics and Mathematical Physics》2014,54(9):1441-1458
A nonlocal boundary value problem for a third-order hyperbolic equation with variable coefficients is considered in the one- and multidimensional cases. A priori estimates for the nonlocal problem are obtained in the differential and difference formulations. The estimates imply the stability of the solution with respect to the initial data and the right-hand side on a layer and the convergence of the difference solution to the solution of the differential problem. 相似文献
18.
We consider a problem for a quasilinear hyperbolic equation with a nonlocal condition that contains a retarded argument. By reducing this problem to a nonlinear integrofunctional equation, we prove the existence and uniqueness theorem for its solution. We pose an inverse problem of finding a solution-dependent coefficient of the equation on the basis of additional information on the solution; the information is given at a fixed point in space and is a function of time. We prove the uniqueness theorem for the solution of the inverse problem. The proof is based on the derivation and analysis of an integro-functional equation for the difference of two solutions of the inverse problem. 相似文献
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O. Kh. Masaeva 《Differential Equations》2013,49(12):1518-1523
We study the Dirichlet problem for a nonlocal wave equation in a rectangular domain. We prove the existence and uniqueness of a solution of the problem and show that determining whether the solution is unique can be reduced to determining whether a function of Mittag-Leffler type has real zeros. The obtained uniqueness condition turns into the uniqueness condition for the solution of the Dirichlet problem for the wave equation as the order of the fractional derivative in the equation tends to 2. 相似文献