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1.
V. G. Krotov 《Mathematical Notes》2000,68(2):201-216
In this paper we study the asymptotic behavior of functions defined on domains of a multidimensional real or complex space
when the point tends to the boundary in the approach region with different orders of tangency. The main results are related
to the boundary behavior of functions from Hardy-Sobolev spaces in a multidimensional complex ball and of solutions to elliptic
boundary-value problems in a Lipschitz domain of a real Euclidean space. The methods used are based on two-weighted estimates
for tangential maximal functions in an abstract ball. The boundary of this ball is a space equipped with measure and quasimetric.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 230–248, August, 2000. 相似文献
2.
Shuxing Chen 《Frontiers of Mathematics in China》2007,2(1):87-102
This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic
boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. The
concept on regular characteristics and dissipative boundary conditions are given for quasilinear hyperbolic systems. Under
some assumptions, an existence theorem for such initial boundary value problems is obtained. The theorem can also be applied
to the Euler system of compressible flow.
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Translated from Chinese Annals of Mathematics, Ser. A, 1982, 3(2): 223–232 相似文献
3.
4.
S. D. Troitskaya 《Mathematical Notes》1999,65(2):242-252
In the paper we study a boundary value problem for a hyperbolic equation with two independent variables; this problem is a
generalization of the well-known Darboux problem.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 294–306, February, 1999. 相似文献
5.
In this paper we study the Riemann and Hilbert problems of k-monogenic functions. By using Euler operator, we transform the boundary value problem of k-monogenic functions into the boundary value problems of monogenic functions. Then by the Almansi-type theorem of k-monogenic functions, we get the solutions of these problems. 相似文献
6.
The lower bounds of life span of classical solutions to one‐dimensional initial‐Neumann boundary value problems for general quasilinear wave equations
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Wei Han 《Mathematical Methods in the Applied Sciences》2016,39(4):906-929
In this paper, we will study the lower bounds of the life span (the maximal existence time) of solutions to the initial‐boundary value problems with small initial data and zero Neumann boundary data on exterior domain for one‐dimensional general quasilinear wave equations utt?uxx=b(u,Du)uxx+F(u,Du). Our lower bounds of the life span of solutions in the general case and special case are shorter than that of the initial‐Dirichlet boundary value problem for one‐dimensional general quasilinear wave equations. We clarify that although the lower bounds in this paper are same as that in the case of Robin boundary conditions obtained in the earlier paper, however, the results in this paper are not the trivial generalization of that in the case of Robin boundary conditions because the fundamental Lemmas 2.4, 2.5, 2.6, and 2.7, that is, the priori estimates of solutions to initial‐boundary value problems with Neumann boundary conditions, are established differently, and then the specific estimates in this paper are different from that in the case of Robin boundary conditions. Another motivation for the author to write this paper is to show that the well‐posedness of problem 1.1 is the essential precondition of studying the lower bounds of life span of classical solutions to initial‐boundary value problems for general quasilinear wave equations. The lower bound estimates of life span of classical solutions to initial‐boundary value problems is consistent with the actual physical meaning. Finally, we obtain the sharpness on the lower bound of the life span 1.8 in the general case and 1.10 in the special case. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
7.
A. I. Kozhanov 《Mathematical Notes》1999,65(1):59-63
A comparison principle for solutions of the first initial boundary value problem for the generalized Boussinesque equation
with a nonlinear sourceu
t-Δψ(u)-Δu
t+q(u)=0 is established. By using this comparison principle, we prove new existence and nonexistence theorems for solutions of the
first initial boundary value problem in the case of power-law functions ψ (ξ) andq (ξ).
Translated fromMathematicheskie Zametki, Vol. 65, No. 1, pp. 70–75, January, 1999. 相似文献
8.
Yu. A. Konyaev 《Mathematical Notes》1999,65(6):701-704
Singularly perturbed initial boundary value problems are studied for some classes of linear systems of ordinary differential
equations on the semiaxis with an unbounded spectrum of the limit operator. We give a new version of the proof of the existence
of a unique and bounded (as ε→+0) solution for which with the help of the splitting method we construct a uniform asymptotic
expansion on the entire semiaxis and describe all singularities (reflecting the structure of the corresponding boundary layers)
in closed analytic form, including the critical case in which the points of the spectrum of the limit operator can touch the
imaginary axis; this supplements previous results.
Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 831–835, June, 1999. 相似文献
9.
M. Azizov 《Mathematical Notes》1997,62(5):537-548
The exact order of complexity of weakly singular integral equations including logarithmic singularities with periodic and
analytic coefficients is found. This class of equations contains the boundary equations of exterior boundary value problems
for the two-dimensional Helmholtz equation.
Translated fromMatematicheskie Zarnetki, Vol. 62, No. 5, pp. 643–656, November, 1997.
Translated by O. V. Sipacheva 相似文献
10.
In this paper, we define the discrete p-Schrödinger operators on finite networks and discuss the existence of the Dirichlet eigenvalues and their eigenfunctions for the operators. We also provide various equivalent conditions for the existence of positive solutions for Dirichlet boundary value problems for the operators. 相似文献
11.
I. M. Nabiev 《Mathematical Notes》2000,67(3):309-319
For boundary value problems generated by a second-order differential equation with regular nonseparated boundary conditions,
criteria for the eigenvalues to be multiple are given and the relative position of the eigenvalues is studied.
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 369–381, March, 2000. 相似文献
12.
A method for solving Hilbert's boundary value problem with discontinuous coefficients is studied for a function single-valued
and analytic in an annulus in the case in which the solution may have power-law singularities at finitely many points on the
boundary of the annulus. To illustrate the results obtained, we consider an explosion problem for two pinching charges in
a homogenous medium with a circular cylinder lying in the flow caused by the explosion.
Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 135–144, July, 1999. 相似文献
13.
Nikolaos Bournaveas 《偏微分方程通讯》2013,38(7-8):1167-1193
Abstract We show a method to eliminate a type of mixed asymptotics in certain free boundary problems, and give two examples of its application. It appears that these problems cannot be handled by the monotonicity formula of Alt et al. [Alt, H. W., Caffarelli, L. A., Friedman, A. (1984). Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2):431–461] or by the more recent monotonicity formula of Caffarelli et al. [Caffarelli, L. A., Jerison, D., Kenig, C. E. (2002). Some new monotonicity theorems with applications to free boundary problems. Ann. Math. (2) 155(2):369–404]. 相似文献
14.
15.
n阶非线性常微分方程两点及三点边值问题解的存在性的进一步结果 总被引:6,自引:0,他引:6
本文利用上、下解方法讨论了n阶非线性常微分方程y^(n)=f(t,y,y‘…,y^(n-1))满足下列非线性边界条件的边值问题解的存在性。 相似文献
16.
M. Mirsaburov 《Mathematical Notes》2000,67(5):611-617
We consider the boundary-value problem for the Gellerstedt equation
wherem=const > 0, in a mixed region; in contrast to the Tricomi problem, nonlocal conditions pointwise connecting the boundary valuesu(x, y) with the values on an inner curve and on the line of degeneracy are assumed on some arcs of the elliptic part of the boundary,
and a condition with displacement is assumed on the characteristic parts of the boundary. Under certain constraints on the
functions in the boundary conditions, we prove the unique solvability of the problem considered.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 721–729, May, 2000. 相似文献
17.
Jiří Taufer 《Applications of Mathematics》2004,49(2):141-164
The paper is devoted to solving boundary value problems for self-adjoint linear differential equations of 2nth order in the case that the corresponding differential operator is self-adjoint and positive semidefinite. The method proposed consists in transforming the original problem to solving several initial value problems for certain systems of first order ODEs. Even if this approach may be used for quite general linear boundary value problems, the new algorithms described here exploit the special properties of the boundary value problems treated in the paper. As a consequence, we obtain algorithms that are much more effective than similar ones used in the general case. Moreover, it is shown that the algorithms studied here are numerically stable. 相似文献
18.
A boundary value problem for a second-order nonlinear singularly perturbed differential equation is considered for the case
in which there is variation of stability caused by the intersection of roots of the degenerate equation. By the method of
differential inequalities, we prove the existence of a solution such that the limit solution is nonsmooth.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 354–362, March, 1998.
This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-00694. 相似文献
19.
Raúl Castillo Pérez Vladislav V. Kravchenko Rabindranath Reséndiz Vázquez 《Mathematical Methods in the Applied Sciences》2011,34(4):455-468
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad + qin the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q with the aid of pseudoanalytic function theory a complete system of null solutions of the operator can be constructed following a simple algorithm consisting in recursive integration. This system of solutions is used for solving boundary value and spectral problems for the operator D in bounded simply connected domains. We study theoretical and numerical aspects of the method. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
20.
Qingliu Yao 《Applicable analysis》2013,92(1):97-107
The existence of m positive solutions is proven for a nonlinear fourth-order boundary value problem with two parameters, where m is an arbitrary natural number. This kind of fourth-order boundary value problems usually describes the equilibrium state of elastic beam where both ends are simply supported. The main ingredient is Krasnosel'skii fixed point theorem of cone expansion–compression type. 相似文献