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1.
We are interested in parabolic problems with L1 data of the type
with i, j=0, 1, (i, j) (0, 0), 0 = 0 and 1 = 1. Here, is an open bounded subset of
with regular boundary and
is a Caratheodory function satisfying the classical Leray-Lions conditions and is a monotone graph in
with closed domain and such that
We study these evolution problems from the point of view of semi-group theory, then we identify the generalized solution of the associated Cauchy problem with the entropy solution of
in the usual sense introduced in [5]. 相似文献
2.
Zhaoli Liu Zhi-Qiang Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(4):609-629
We obtain the existence of infinitely many nodal solutions for the Schrödinger type equation on
with
Here,
The nonlinearity f is symmetric in the sense of being odd in u, and may involve a combination of concave and convex terms.Received: November 11, 2003; revised: December 12, 2004Supported by NSFC:10441003 相似文献
3.
In this paper, we give an Lp-Lq-version of Morgans theorem for the Dunkl-Bessel transform
on
More precisely, we prove that for all
and
then for all measurable function f on
the conditions
and
imply f = 0, if and only if
where
are the Lebesgue spaces associated with the Dunkl-Bessel transform.Received: November 21, 2003 Revised: April 26, 2004 Accepted: May 28, 2004 相似文献
4.
Estimates for deviations are established for a large class of linear methods of approximation of periodic functions by linear combinations of moduli of continuity of different orders. These estimates are sharp in the sense of constants in the uniform and integral metrics. In particular, the following assertion concerning approximation by splines is proved: Suppose that
is odd,
. Then
moreover, for
it is impossible to decrease the constants on
. Here,
are some explicitly constructed constants,
is the modulus of continuity of order r for the function f, and
are explicitly constructed linear operators with the values in the space of periodic splines of degree
of minimal defect with 2n equidistant interpolation points. This assertion implies the sharp Jackson-type inequality
. Bibliography: 17 titles. 相似文献
5.
Noriko Mizoguchi 《Mathematische Annalen》2007,339(4):839-877
A solution u of a Cauchy problem for a semilinear heat equation
is said to undergo Type II blowup at t = T if lim sup Let be the radially symmetric singular steady state. Suppose that is a radially symmetric function such that and (u
0)
t
change sign at most finitely many times. We determine the exact blowup rate of Type II blowup solution with initial data
u
0 in the case of p > p
L
, where p
L
is the Lepin exponent. 相似文献
6.
Let u(x) xR
q
be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p
x, (·) be the density of an R
q
valued canonical normal random variable with mean x and variance and let {G
x, ; (x, )R
q
×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R
q
is said to be in
with respect to u, if
When
, a multiple Wick product chaos
is defined to be the limit in L
2, as 0, of
where
,
denotes the Wick product of the m
j
normal random variables
.Consider also the associated decoupled chaos processes
,
defined as the limit in L
2, as 0, of
where
are independent copies of G
x,.Define
Note that a neighborhood of the diagonals of
in
is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is:
Theorem A. If
is continuous on (R
q
)
r
for all
then
is continuous on
.When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of
on (R
q
)
r
. Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes. 相似文献
7.
A generalized interpolation polynomial with a base function
and node coefficients
, is a polynomial of the form
where the system of functions
forms a Chebyshev system on [a,b]. In this article, we show that by using the polynomials g(x) one can construct both adaptive quadrature formulas that optimize the quadrature error and piecewise-smooth stable solutions of the Cauchy problem. 相似文献
8.
B. Scarpellini 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(3):412-438
In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form
It is shown that this equilibrium is Ljapounov stable under small perturbations in
where
provided that the parameters a, b, , are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data techniques.Received: February 5, 2003; revised: September 29, 2003Dedicated to Prof. H. Amann on the occasion of his 65. birthday 相似文献
9.
This paper considers the approximation of the Kantorovich–Shepard operators in
spaces for
. For
the Kantorovich–Shepard operators
are defined by (1.1). Then
where
is a positive number depending only on
and , and $$ \varepsilon_{n} =\cases{ n^{-1}, & if \
2$$
" align="middle" border="0">
; \cr\nosm n^{-1}\log n, & if \
; \cr\nosm n^{1-\lambda}, & if \
. \cr} $$ 相似文献
10.
Changjiang Zhu Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(6):994-1014
In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects
with initial data
where and are positive constants such that < 1, < (1–). Through constructing a correct function
defined by (2.13) and using the energy method, we show
as
and the solutions decay with exponential rates. The same problem is studied by Tang and Zhao [10] for the case of (±, ±) = (0,0).Received: November 18, 2003 相似文献
((E)) |
((I)) |
11.
12.
Václav Tryhuk 《Czechoslovak Mathematical Journal》2000,50(3):509-518
The paper describes the general form of an ordinary differential equation of the order n + 1 (n 1) which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form
where
are given functions,
is solved on
. 相似文献
13.
Elena Cordero Stevan Pilipović Luigi Rodino Nenad Teofanov 《Mediterranean Journal of Mathematics》2005,2(4):381-394
We study localization operators within the framework of ultradistributions. More precisely, given a symbol a and two windows φ1, φ2, we investigate the multilinear mapping from
to the localization operator
Results are formulated in terms of modulation spaces with weights which may have exponential growth. We give sufficient and
necessary conditions for
a to be bounded or to belong to a Schatten class. As an application, we study symbols defined by ultra-distributions with
compact support, that give trace class localization operators. 相似文献
14.
Consider the Dirichlet problem for the parabolic equation
in
, where
$\Omega$ is a bounded domain in
and f has superlinear subcritical growth in u.
If f is independent of t and satisfies some
additional conditions then using a dynamical method we find multiple (three, six or infinitely many) nontrivial
stationary solutions. If f has the form
where m is periodic, positive and m,g satisfy some technical
conditions then we prove the existence of a positive periodic solution and
we provide a locally uniform bound for all global solutions. 相似文献
15.
In this note we prove that the Laplacian with generalized Wentzell boundary
conditions on an open bounded regular domain in
defined by
generates an analytic semigroup of angle
on
for every > 0 and
(for the definition of
cf. (1.3)).Received: 13 July 2002 相似文献
16.
J. Tervo 《Aequationes Mathematicae》1990,40(1):201-234
The paper deals with the minimal and the maximal realizations (L
w
)~ and (L
w
):L
2L
2 of linear operators of Weyl type
} dy} } \right)d\xi }$$
" align="middle" vspace="20%" border="0"> 相似文献
17.
S. Yu. Orevkov 《Mathematical Notes》2000,68(5-6):588-593
Dehornoy constructed a right invariant order on the braid group B
n uniquely defined by the condition
1{\text{ if }}\beta _0 ,\beta _1$$
" align="middle" border="0">
are words in
. A braid is called strongly positive if
1$$
" align="middle" border="0">
for any
. In the present paper it is proved that the braid
is strongly positive if the word
does not contain
. We also provide a geometric proof of the result by Burckel and Laver that the standard generators of a braid group are strongly positive. Finally, we discuss relations between the right invariant order and quasipositivity. 相似文献
18.
A. V. Latyshev 《Theoretical and Mathematical Physics》1993,97(2):1299-1311
Exact solutions are obtained for the first time for the half-space boundary-value problem for the vector model kinetic equations
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