共查询到20条相似文献,搜索用时 531 毫秒
1.
On the basis of the exact solution of the linear Dirichlet problem
,
we obtain conditions for the solvability of the corresponding Dirichlet problem for the quasilinear equation u
tt – u
xx = f(x, t, u, u
t). 相似文献
2.
W. M. Oliva J. C. F. de Oliveira J. Solà-Morales 《NoDEA : Nonlinear Differential Equations and Applications》1994,1(4):365-387
A semi-implicit discretization on time of the one-dimensional parabolic equationu
t=uxx+f(u(x)), (x, t) (0, 1)×R+, with Dirichlet boundary conditions, gives rise to an infinite dimensional map
h
(u): starting from
, we define a discrete flow on the Hilbert spaceH
0
1
(0, 1), given by
h
(u) = (I -h)-1(u+h f o u). The corresponding flow has gradient structure, compact attractor, lap number and Morse-Smale properties and structural stability with respect to the attractor.With partial support of FAPESP proc. 90/3918-5.and* Partialy supported by Projeto BID-USP-IME.With partial support of DGICYT (Spain) under Project PB91-0497. 相似文献
3.
Ridgway Scott 《Numerische Mathematik》1973,21(4):317-327
Convergence of the finite element solutionu
h
of the Dirichlet problem u= is proved, where is the Dirac -function (unit impulse). In two dimensions, the Green's function (fundamental solution)u lies outsideH
1, but we are able to prove that
. Since the singularity ofu is logarithmic, we conclude that in two dimensions the function log can be approximated inL
2 near the origin by piecewise linear functions with an errorO (h). We also consider the Dirichlet problem u=f, wheref is piecewise smooth but discontinuous along some curve. In this case,u just fails to be inH
5/2, but as with the approximation to the Green's function, we prove the full rate of convergence:u–u
h
1=O (h
8/2) with, say, piecewise quadratics. 相似文献
4.
In this paper, we give weak regularity theorems on P of u~ε(x, P), where u~ε(x, P)is the viscosity solution of the cell problem H_ε(P D_xu~ε, x)=H_ε(P). 相似文献
5.
On characterizing the solution sets of pseudolinear programs 总被引:8,自引:0,他引:8
This paper provides several new and simple characterizations of the solution sets of pseudolinear programs. By means of the basic properties of pseudolinearity, the solution set of a pseudolinear program is characterized, for instance, by the equality that
, for each feasible pointx, where
is in the solution set. As a consequence, we give characterizations of both the solution set and the boundedness of the solution set of a linear fractional program. 相似文献
6.
P. G. Grinevich 《Theoretical and Mathematical Physics》1994,99(2):599-605
The direct and the inverse scattering problems for the heat-conductivity operator
are studied for the following class of potentials:u(x,y)=u
o
(x,y)+u
1(x,y), whereu
o
(x,y) is a nonsingular real finite-gap potential andu
1(x,y) decays sufficiently fast asx
2+y2. We show that the scattering data for such potentials is the
data on the Riemann surface corresponding to the potentialu
o
(x,y). The scattering data corresponding to real potentials is characterized and it is proved that the inverse problem corresponding to such data has a unique nonsingular solution without the small norm assumption. Analogs of these results for the fixed negative energy scattering problem for the two-dimensional time-independent Schrödinger operator
are obtained.L. D. Landau Institute for Theoretical Physics, Kosygina 2, GSP-1, Moscow 177940, Russia. E-mail: pgg@cpd.landau.free.net. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 300–308, May, 1994. 相似文献
7.
In this paper, we establish lower bounds for n-term approximations in the metric of L
2(I
2
) of characteristic functions of plane convex subsets of the square I
2
with respect to arbitrary orthogonal systems. It is shown that, as n, these bounds cannot decrease more rapidly than
. 相似文献
8.
Mario Wschebor 《Probability Theory and Related Fields》1982,60(3):393-401
Summary Let {x(t): tR
d} a stochastic process with parameter in R
d, and u a fixed real number. Denote by C
u, Au, Bu respectively the random sets {t: x(t)= u}, {t: x(t)}, {t: x(t)>u}. The paper contains two main results for processes with continuously differentiable paths plus some additional requirements: First, a formula for the expectation of Q
T(Au) and Q
T(Bu), where for a given bounded open set T in R
d, QT(B) denotes the perimeter of B relative to T and second, sufficient conditions on the process, so that it does not have local extrema on the barrier u. The second result can also be used to interpret the first in terms of C
u. 相似文献
9.
R. G. Jeroslow 《Journal of Optimization Theory and Applications》1980,30(3):339-351
Any optimization problem in a finite structure can be represented as an integer or mixed-integer program in integral quantities.We show that, when an optimization problem on an unbounded structure has such a representation, it is very close to a linear programming problem, in the specific sense described in the following results. We also show that, if an optimization problem has such a representation, no more thann+2 equality constraints need be used, wheren is the number of variables of the problem.We obtain a necessary and sufficient condition for a functionf:SZ, withS
Z
n
, to have a rational model in Meyer's sense, and show that Ibaraki models are a proper subset of Meyer models.This research was supported by NSF Grant No. GP-37510X1 and ONR Contract No. N00014-75-C0621, NR047-048. 相似文献
10.
We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u
tt
=c
2
u
xx
, given by
相似文献
11.
Classical theorems on differential inequalities [1, 2, 3] are generalized for initial value problems of the kind
and
where
is a singular Volterra operator,
is continuous and positive on ]a, b],
is a norm in R
n, and [u]+ and [u]– are respectively the positive and the negative part of the vector u R
n. 相似文献
12.
We consider one-phase Stefan problems for the equation
u
i
=u
xx
+u
1+a
(>0)in one-dimensional space, which have blow-up solutions for a larger initial data. In this paper, the global existence result for our problem is proved by using energy inequalities. More precisely, if >1 an initial function is sufficiently small, then the free boundary is bounded and
decay in exponential order. 相似文献
13.
The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR
+
n
ofR
n intoR
n can be written as the system of equationsF(x, y) = 0 and(x, y) R
+
2n
, whereF denotes the mapping from the nonnegative orthantR
+
2n
ofR
2n intoR
+
n
× Rn defined byF(x, y) = (x
1y1,,xnyn, f1(x) – y1,, fn(x) – yn) for every(x, y) R
+
2n
. Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR
+
2n
ontoR
+
n
× Rn. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x
0, y0) and(x, y) R
+
2n
from an arbitrary initial point(x
0, y0) R
+
2n
witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices. 相似文献
14.
O. L. Mangasarian 《Mathematical Programming》1990,48(1-3):437-445
Error bounds and upper Lipschitz continuity results are given for monotone linear complementarity problems with a nondegenerate solution. The existence of a nondegenerate solution considerably simplifies the error bounds compared with problems for which all solutions are degenerate. Thus when a point satisfies the linear inequalities of a nondegenerate complementarity problem, the residual that bounds the distance from a solution point consists of the complementarity condition alone, whereas for degenerate problems this residual cannot bound the distance to a solution without adding the square root of the complementarity condition to it. This and other simplified results are a consequence of the polyhedral characterization of the solution set as the intersection of the feasible region {zMz + q 0, z 0} with a single linear affine inequality constraint.This material is based on research supported by National Science Foundation Grants CCR-8723091 and DCR-8521228 and Air Force Office of Scientific Research Grant AFOSR-86-0172. 相似文献
15.
Yong-hui Wu 《Mathematical Methods in the Applied Sciences》1997,20(11):933-943
In this paper, we consider the Cauchy problem: (ECP) ut−Δu+p(x)u=u(x,t)∫u2(y,t)/∣x−y∣dy; x∈ℝ3, t>0, u(x, 0)=u0(x)⩾0 x∈ℝ3, (0.2) The stationary problem for (ECP) is the famous Choquard–Pekar problem, and it has a unique positive solution ū(x) as long as p(x) is radial, continuous in ℝ3, p(x)⩾ā>0, and lim∣x∣→∞p(x)=p¯>0. In this paper, we prove that if the initial data 0⩽u0(x)⩽(≢)ū(x), then the corresponding solution u(x, t) exists globally and it tends to the zero steady-state solution as t→∞, if u0(x)⩾(≢)ū(x), then the solution u(x,t) blows up in finite time. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献
16.
We present a characterization of the normal optimal solution of the linear program given in canonical form max{c
tx: Ax = b, x 0}. (P) We show thatx
* is the optimal solution of (P), of minimal norm, if and only if there exists anR > 0 such that, for eachr R, we havex
* = (rc – Atr)+. Thus, we can findx
* by solving the following equation for
r A(rc – Atr)+ = b. Moreover,(1/r)
r then converges to a solution of the dual program.On leave from The University of Alberta, Edmonton, Canada. Research partially supported by the National Science and Engineering Research Council of Canada. 相似文献
17.
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
18.
Given ringsR with prime power characteristicp
k
, quasivarieties (R) of lattices generated by lattices of submodules ofR-modules are studied. An algebra of expressionsd not dependent onR is developed, such that each suchd uniquely determines a two-sides ideald
R
ofR. The main technical result is that (R)
(S) makes all implications of the formd
s
=S dR=R true, for any such expressiond. The proof makes use of the known equivalence between (R)
(S) and existence of an exact embedding functorR-Mod S
-Mod. Fork 2, the ordered setW(p
k
) of all lattice quasivarieties (R),R having characteristic p
K
, is shown to be large and complicated, with ascending and descending chains and antichains having continuously many elements. More precisely,W(p
k
) has a subset which is order isomorphic to the Boolean algebra of all subsets of a denumerably infinite set. Also, given any prime powerp
k
,k 2, a ringR can be constructed so that (R) and (R
op) for the opposite ringR
op are distinct elements ofW(p
k
).Presented by R. Freese.Research partially supported by Hungarian National Foundation for Scientific Research grant no. 1903. 相似文献
19.
Olav Kallenberg 《Probability Theory and Related Fields》1988,77(3):415-455
Summary Consider an array X = (X
ij
,i,jN) of random variables, and let U=(U
ij
) and V=(V
ij
) be orthogonal transformations affecting only finitely many coordinates. Say that X is separately rotatable if
for arbitrary U and V, and jointly rotatable if this holds with U=V. Restricting U and V to the class of permutations, we get instead the property of separate or joint exchangeability. Processes on
+
2
, + × [0,1] or [0, 1]2 are said to be separately or jointly exchangeable, if the arrays of increments over arbitrary square grids have these properties. For some of the above cases, explicit representations have recently been obtained, independently, by Aldous and Hoover. The aim of the present paper is to continue the work of these authors by deriving some new representations, and by solving the associated uniqueness and continuity problems.Research suported by the Air Force Office of Scientific Research Grant No. F 49620 85C 0144 相似文献
20.
Some laws in physics describe the change of a flux and are represented by parabolic equations of the form (*) \documentclass{article}\pagestyle{empty}\begin{document}$$\frac{{\partial u}}{{\partial t}}=\frac{\partial}{{\partial x_j }}(\eta \frac{{\partial u}}{{ax_j}}-vju),$$\end{document} j≤m, where η and vj are functions of both space and time. We show under quite general assumptions that the solutions of equation (*) with homogeneous Dirichlet boundary conditions and initial condition u(x, 0) = uo(x) satisfy The decay rate d > 0 only depends on bounds for η, v and G § Rm the spatial domain, while the constant c depends additionally on which norm is considered. For the solutions of equation (*) with homogeneous Neumann boundary conditions and initial condition u0(x) ≥ 0 we derive bounds d1u1 ≤ u(x, t) ≤ d2u2, Where di, i = 1, 2, depend on bounds for η, v and G, and the ui are bounds on the initial condition u0. 相似文献
|