共查询到20条相似文献,搜索用时 46 毫秒
1.
Yu. B. Dmytryshyn 《Journal of Mathematical Sciences》2010,171(4):474-489
We study a dynamic boundary-value problem without initial conditions for linear and almost linear parabolic equations. First,
we establish conditions for the existence of a unique solution of a problem without initial conditions for a certain abstract
implicit evolution equation in the class of functions with exponential behavior as t → −∞. Then, using these results, we prove the existence of a unique solution of the original problem in the class of functions
with exponential behavior at infinity. 相似文献
2.
Monica Marras Stella Vernier Piro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,203(1):766-779
We investigate the behavior of the solution of a nonlinear heat problem, when Robin conditions are prescribed on the boundary
∂Ω × (t > 0), Ω a bounded R
2 domain. We determine conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain
an exponential decay bound for the solution and its gradient. 相似文献
3.
Monica Marras Stella Vernier Piro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):766-779
We investigate the behavior of the solution of a nonlinear heat problem, when Robin conditions are prescribed on the boundary
∂Ω × (t > 0), Ω a bounded R
2 domain. We determine conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain
an exponential decay bound for the solution and its gradient.
Supported by the University of Cagliari. 相似文献
4.
Refinable functions with exponential decay arise from applications such as the Butterworth filters in signal processing. Refinable
functions with exponential decay also play an important role in the study of Riesz bases of wavelets generated from multiresolution
analysis. A fundamental problem is whether the standard solution of a refinement equation with an exponentially decaying mask
has exponential decay. We investigate this fundamental problem by considering cascade algorithms in weighted L
p
spaces (1≤p≤∞). We give some sufficient conditions for the cascade algorithm associated with an exponentially decaying mask to converge
in weighted L
p
spaces. Consequently, we prove that the refinable functions associated with the Butterworth filters are continuous functions
with exponential decay. By analyzing spectral properties of the transition operator associated with an exponentially decaying
mask, we find a characterization for the corresponding refinable function to lie in weighted L
2 spaces. The general theory is applied to an interesting example of bivariate refinable functions with exponential decay,
which can be viewed as an extension of the Butterworth filters. 相似文献
5.
We consider the system of m linear equations in n integer variables Ax = d and give sufficient conditions for the uniqueness of its integer solution x ∈ {−1, 1}
n
by reformulating the problem as a linear program. Necessary and sufficient uniqueness characterizations of ordinary linear
programming solutions are utilized to obtain sufficient uniqueness conditions such as the intersection of the kernel of A and the dual cone of a diagonal matrix of ±1’s is the origin in R
n
. This generalizes the well known condition that ker(A) = 0 for the uniqueness of a non-integer solution x of Ax = d. A zero maximum of a single linear program ensures the uniqueness of a given integer solution of a linear equation. 相似文献
6.
V. I. Bernik V. V. Beresnevich P. B. Vasylyshyn B. I. Ptashnyk 《Ukrainian Mathematical Journal》1999,51(10):1476-1483
We establish conditions for the unique solvability of a multipoint (with respect to the time coordinate) problem with multiple
nodes for linear hyperbolic equations with constant coefficients in the class of functions periodic in the space variable.
We prove metric statements concerning lower bounds of small denominators that appear in the course of construction of a solution
of the problem.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1311–1316, October, 1999. 相似文献
7.
B. V. Gera 《Journal of Mathematical Sciences》1997,86(2):2578-2584
We propose a statement and computational scheme for the inverse problem of recovering the temperature field and the moisture
distribution in a body with incompletely known initial conditions. We give additional relations on the integral values of
the unknown functions and introduce a test for the choice of a unique solution of the problem from the set of admissible temperature
and moisture functions. We state conditions for independence of the additional data and obtain systems of equations and conditions
that close the initial indeterminate problem. We study in detail the example of heat-moisture conduction in a layer.
Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 66–73. 相似文献
8.
H. P. Lopushans’ka 《Ukrainian Mathematical Journal》2007,59(12):1885-1901
We establish conditions for the nonlinear part of a quasilinear elliptic equation of order 2m with linear principal part under which a solution regular inside a domain and belonging to a certain weighted L
1-space takes boundary values in the space of generalized functions.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 12, pp. 1674–1688, December, 2007. 相似文献
9.
We use the apparatus of RITZ-fractions to improve the convergence of series that represent the formal solution of linear differential equations with parameter
under boundary or initial conditions. We establish conditions for the existence of this solution in the case where the parameter
of the equation tends to infinity. The case of a small parameter is also considered.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 679–686, May, 1998. 相似文献
10.
R. Hakl 《Ukrainian Mathematical Journal》2008,60(3):481-494
For a linear functional differential equation of the third order {fx481-01}, we establish the theorems on existence and uniqueness
of a solution satisfying the conditions {fx481-02}. Here, ℓ is a linear continuous operator transforming the space C([0, ω]; R) into the space L([0, ω]; R) and q ∈ L([0, ω]; R). The problem of nonnegativity of the solution of the analyzed boundary-value problem is also studied.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 3, pp. 413–425, March, 2008. 相似文献
11.
In this paper, we investigate a third-order linear differential equation with three additional conditions. We find a solution
to this problem and give a formula and an existence condition for Green’s function. We compare two Green’s functions for two
such problems with different additional conditions: nonlocal and classical boundary conditions. Formula applications are shown
by examples. 相似文献
12.
Construction of the solutions of linear hyperbolic systems using laguerre geometric-optic expansions
A. N. Gorechko 《Journal of Mathematical Sciences》1998,90(2):1936-1940
We discuss a technique for expanding the solution of a linear hyperbolic system of differential equations in a series of Laguerre
functions behind the wave front. Solving the original linear system is reduced to solving the eikonal equation that describes
the behavior of the wave front and a sequence of transfer systems that describe the Laguerre spectrum. The application of
the technique is illustrated using the examples of one-dimensional acoustic and thermoelastic waves.
Translated fromMatemetichni Metodi ta Fiziko-Mekhanichni Polya. Vol. 40, No. 2, 1997, pp. 39–43. 相似文献
13.
We investigate the first mixed problem for a quasilinear hyperbolic equation of the second order with power nonlinearity in
a domain unbounded with respect to the space variables. The case of arbitrarily many space variables is considered. We establish
conditions for the existence and uniqueness of a solution of this problem independent of the behavior of the solution as |x| → + ∞. The indicated classes of existence and uniqueness are the spaces of locally integrable functions, and, furthermore,
the dimension of the domain does not limit the order of nonlinearity.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1523–1531, November, 2007. 相似文献
14.
We study in this paper the global existence and exponential decay of solutions of the non‐linear unidimensional wave equation with a viscoelastic boundary condition. We prove that the dissipation induced by the memory effect is strong enough to secure global estimates, which allow us to show existence of global smooth solution for small initial data. We also prove that the solution decays exponentially provided the resolvent kernel of the relaxation function, k decays exponentially. When k decays polynomially, the solution decays polynomially and with the same rate. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
15.
S. S. Marchenkov 《Mathematical Notes》1999,66(5):577-584
For continuous functions specified on the Baire space, conditions for the representability of a function of several variables
as a superposition of functions of a smaller number of variables are considered. With the use of linear functions of the form
(1+α)t, a boundary value of the modulus of continuity separating the positive from the negative solution of the problem is found.
For the case in which the problem has a negative solution, a constructive method for obtaining (n+1)-variable continuous functions with modulus of continuity ϕ(t) that are not representable as superposition ofn-variable continuous functions with the same modulus of continuity ϕ(t) is suggested.
Translated fromMatermaticheskie Zametki, Vol. 66, No. 5, pp. 696–705, November, 1999. 相似文献
16.
Yang Zhijian 《Mathematical Methods in the Applied Sciences》2002,25(10):825-833
We consider the blowup of solutions of the initial boundary value problem for a class of non‐linear evolution equations with non‐linear damping and source terms. By using the energy compensation method, we prove that when p>max{m, α}, where m, α and p are non‐negative real numbers and m+1, α+1, p+1 are, respectively, the growth orders of the non‐linear strain terms, damping term and source term, under the appropriate conditions, any weak solution of the above‐mentioned problem blows up in finite time. Comparison of the results with the previous ones shows that there exist some clear condition boundaries similar to thresholds among the growth orders of the non‐linear terms, the states of the initial energy and the existence and non‐existence of global weak solutions. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
17.
V. N. Denisov 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):91-103
We obtain sharp sufficient conditions on the growth of lower order coefficients of a second-order parabolic equation under
which a solution to the Cauchy problem stabilizes to zero uniformly in x on every compact set K ∈ ℝ
N
in some classes of growing initial functions. 相似文献
18.
S. K. Persidskii 《Journal of Mathematical Sciences》1996,82(3):3399-3401
We propose a solution of the problem inverse to the well-known problem of constructing Lyapunov functions for linear systems
with constant coefficients, making it possible to obtain new conditions for positive- and negative-definiteness of forms of
degrees two and three in an arbitrary octant of the space Rn.
Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 3–6. 相似文献
19.
We propose an approach to the approximation of solutions of problems for the heat-conduction equation without initial or boundary-value
conditions. The solution is given as a sum of odd and even functions, and this allows one to reconstruct conditions missed
in the initial setting of the problem. The method is illustrated with test examples. Bibliography: 1 title.
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 49–53. 相似文献
20.
We investigate one stage stochastic multiobjective optimization problems where the objectives are the expected values of random
functions. Assuming that the closed form of the expected values is difficult to obtain, we apply the well known Sample Average
Approximation (SAA) method to solve it. We propose a smoothing infinity norm scalarization approach to solve the SAA problem
and analyse the convergence of efficient solution of the SAA problem to the original problem as sample sizes increase. Under
some moderate conditions, we show that, with probability approaching one exponentially fast with the increase of sample size,
an ϵ-optimal solution to the SAA problem becomes an ϵ-optimal solution to its true counterpart. Moreover, under second order growth conditions, we show that an efficient point
of the smoothed problem approximates an efficient solution of the true problem at a linear rate. Finally, we describe some
numerical experiments on some stochastic multiobjective optimization problems and report preliminary results. 相似文献