共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
Magdalena Piszczek 《Aequationes Mathematicae》2014,88(1-2):163-168
We present a result concerning the hyperstability of the general linear equation. Namely, we show that a function satisfying the equation approximately must be actually a solution to it. 相似文献
3.
Janusz Brzdȩk 《Aequationes Mathematicae》2013,86(3):255-267
We present some simple observations on hyperstability for the Cauchy equation on a restricted domain. Namely, we show that (under some weak natural assumptions) functions that satisfy the equation approximately (in some sense), must be actually solutions to it. In this way we demonstrate in particular that hyperstability is not a very exceptional phenomenon as it has been considered so far. We also provide some simple examples of applications of those results. 相似文献
4.
5.
Richard E. Ewing 《Journal of Mathematical Analysis and Applications》1979,71(1):167-186
Numerical approximation of the solution of the Cauchy problem for the linear parabolic partial differential equation is considered. The problem: (p(x)ux)x ? q(x)u = p(x)ut, 0 < x < 1,0 < t? T; ; ; p(0) ux(0, t) = g(t), 0 < t0 ? t ? T, is ill-posed in the sense of Hadamard. Complex variable and Dirichlet series techniques are used to establish Hölder continuous dependence of the solution upon the data under the additional assumption of a known uniform bound for ¦ u(x, t)¦ when 0 ? x ? 1 and 0 ? t ? T. Numerical results are obtained for the problem where the data ?1, ?2 and g are known only approximately. 相似文献
6.
7.
Our purpose is to investigate criteria for hyperstability of linear type functional equations. We prove that a function satisfying the equation approximately in some sense, must be a solution of it. We give some conditions on coefficients of the functional equation and a control function which guarantee hyperstability. Moreover, we show how our outcomes may be used to check whether the particular functional equation is hyperstable. Some relevant examples of applications are presented. 相似文献
8.
A variational formulation of the Cauchy problem for the Laplaceequation is studied. An efficient conjugate gradient method based on an optimal-order stopping criterion is presented together with its numerical implementation based on the boundary-element method. Several numerical examples involving smooth or non-smooth geometries and over-, equally, or under-specified Cauchy dataare discussed. The numerical results show that the numericalsolution is convergent with respect to increasing the numberof boundary elements and stable with respect to decreasingthe amount of noise included in the input Cauchy data.
Received 2 November, 1999. Revised 4 March, 2000. 相似文献
9.
10.
11.
12.
Derchyi Wu 《Journal of Functional Analysis》2009,256(1):215-257
We generalize the results of [J. Villarroel, The inverse problem for Ward's system, Stud. Appl. Math. 83 (1990) 211-222; A.S. Fokas, T.A. Ioannidou, The inverse spectral theory for the Ward equation and for the 2+1 chiral model, Comm. Appl. Anal. 5 (2001) 235-246; B. Dai, C.L. Terng, K. Uhlenbeck, On the space-time Monopole equation, arXiv:math.DG/0602607] to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data. 相似文献
13.
I. M. Plaksina 《Russian Mathematics (Iz VUZ)》2013,57(10):13-18
We study first-order functional differential equations which are singular in the independent variable, establish criteria for the constant sign property of the Cauchy function, and prove an assertion analogous to the Vallée-Poussin theorem. 相似文献
14.
15.
Wei Yan Yongsheng Li Yimin Zhang 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):1157-1169
In this paper we consider the Cauchy problem for the Novikov equation. We prove that the Cauchy problem for the Novikov equation is not locally well-posed in the Sobolev spaces ${H^s(\mathfrak{R})}$ with ${s < \frac{3}{2}}$ in the sense that its solutions do not depend uniformly continuously on the initial data. Since the Cauchy problem for the Novikov equation is locally well-posed in ${H^{s}(\mathfrak{R})}$ with s > 3/2 in the sense of Hadamard, our result implies that s = 3/2 is the critical Sobolev index for well-posedness. We also present two blow-up results of strong solution to the Cauchy problem for the Novikov equation in ${H^{s}(\mathfrak{R})}$ with s > 3/2. 相似文献
16.
17.
Ciplea Sorina Anamaria Lungu Nicolaie Marian Daniela Rassias Themistocles M. 《Aequationes Mathematicae》2023,97(4):649-657
Aequationes mathematicae - In this paper we will study Hyers-Ulam stability for a general linear partial differential equation of first order in a Banach space. 相似文献
18.
19.
No Abstract.
RID="h1"
ID="h1"Dedicated to Ph. Bénilan 相似文献