共查询到20条相似文献,搜索用时 15 毫秒
1.
Wolfgang Arendt 《Positivity》2008,12(1):25-44
Extending results of Davies and of Keicher on ℓp we show that the peripheral point spectrum of the generator of a positive bounded C0-semigroup of kernel operators on Lp is reduced to 0. It is shown that this implies convergence to an equilibrium if the semigroup is also irreducible and the
fixed space non-trivial. The results are applied to elliptic operators.
Dedicated to the memory of H.H. Schaefer 相似文献
2.
Markus Biegert 《Journal of Differential Equations》2009,247(7):1949-698
Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has
3.
We prove existence and (in some special case) uniqueness of an invariant measure for the transition semigroup associated with the stochastic wave equations with nonlinear dissipative damping. 相似文献
4.
5.
Following the recent progress in understanding the abstract setting for Friedrichs symmetric positive systems by Ern, Guermond and Caplain (2007) [8], as well as Antoni? and Burazin (2010) [3], an attempt is made to relate these results to the classical Friedrichs theory.A comparison of two approaches, via the trace operator and the boundary operator, has been made, favouring the latter. Finally, a particular set of sufficient conditions for a boundary matrix field to define a boundary operator in that case is given, and the applicability of this procedure in realistic situations is shown by examples. 相似文献
6.
Željko Čučković 《Integral Equations and Operator Theory》2007,59(3):345-353
We study finite rank perturbations of the Brown-Halmos type results involving products of Toeplitz operators acting on the
Bergman space.
相似文献
7.
Rosalba Di Vincenzo 《Mediterranean Journal of Mathematics》2007,4(1):119-126
Strong solvability in Sobolev spaces is proved for a unilateral boundary value problem for nonlinear parabolic operators.
The operator is assumed to be of Carathéodory type and to satisfy a suitable ellipticity condition; only measurability with
respect to the independent variable X is required.
The main tools of the proof are an estimate for the second derivatives of functions which satisfy the unilateral boundary
conditions and the monotonicity of the operator − u
t
with respect to Δu for the same functions. 相似文献
8.
Harold Widom 《Integral Equations and Operator Theory》2007,57(1):133-151
The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated
Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible) and in singular
cases. This paper treats two cases where the symbol of the Wiener-Hopf operator has Fisher-Hartwig singularities, one double
zero or two simple zeros. We find formulas for the inverse that hold uniformly throughout the underlying interval with very
small error, and formulas for the determinant with very small error. 相似文献
9.
In this paper we consider a class of integral operators whose kernels
satisfy certain generalizations of Hörmander condition and establish their
regularity results. 相似文献
10.
Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4167-4176
We consider the inverse time problem for the nonlinear heat equation in the form
11.
About a construction and some analysis of time inhomogeneous diffusions on monotonely moving domains
Francesco Russo 《Journal of Functional Analysis》2005,221(1):37-82
We construct and analyze in a very general way time inhomogeneous (possibly also degenerate or reflected) diffusions in monotonely moving domains E⊂R×Rd, i.e. if Et?{x∈Rd|(t,x)∈E}, t∈R, then either Es⊂Et, ∀s?t, or Es⊃Et, ∀s?t, s,t∈R. Our major tool is a further developed L2(E,m)-analysis with well chosen reference measure m. Among few examples of completely different kinds, such as e.g. singular diffusions with reflection on moving Lipschitz domains in Rd, non-conservative and exponential time scale diffusions, degenerate time inhomogeneous diffusions, we present an application to what we name skew Bessel process on γ. Here γ is either a monotonic function or a continuous Sobolev function. These diffusions form a natural generalization of the classical Bessel processes and skew Brownian motions, where the local time refers to the constant function γ≡0. 相似文献
12.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):1966-1972
The nonlinear backward Cauchy problem
ut+Au(t)=f(u(t)),u(T)=φ, 相似文献
13.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3479-3488
A nonlinear backward heat problem for an infinite strip is considered. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we use the Fourier regularization method to solve the problem. Some sharp estimates of the error between the exact solution and its regularization approximation are given. 相似文献
14.
A. Rogozhin 《Integral Equations and Operator Theory》2007,57(2):283-301
In this paper we estimate the norm of the Moore-Penrose inverse T(a)+ of a Fredholm Toeplitz operator T(a) with a matrix-valued symbol a∈LN × N∞ defined on the complex unit circle. In particular, we show that in the ”generic case” the strict inequality ||T(a)+|| > ||a−1||∞ holds. Moreover, we discuss the asymptotic behavior of ||T(tra)+|| for
. The results are illustrated by numerical experiments. 相似文献
15.
Products of Toeplitz Operators on the Bergman Space 总被引:1,自引:0,他引:1
Issam Louhichi Elizabeth Strouse Lova Zakariasy 《Integral Equations and Operator Theory》2006,54(4):525-539
In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a
Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic
symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions
for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases
(Theorem 6.4), and then show that almost anything can happen (Theorem 6.7). 相似文献
16.
Triet Minh Le Quan Hoang Pham Trong Duc Dang Tuan Huy Nguyen 《Journal of Computational and Applied Mathematics》2013
We consider the problem of determining the temperature u(x,t), for (x,t)∈[0,π]×[0,T) in the parabolic equation with a time-dependent coefficient. This problem is severely ill-posed, i.e., the solution (if it exists) does not depend continuously on the given data. In this paper, we use a modified method for regularizing the problem and derive an optimal stability estimation. A numerical experiment is presented for illustrating the estimate. 相似文献
17.
Perch Melik-Adamyan 《Complex Analysis and Operator Theory》2007,1(3):423-438
An analog of the Kreĭn–Saakyan formula is derived for any pair of relatively prime self-adjoint extensions of a minimal symmetric
canonical differential operator. This allows us to deduce a trace formula in the matrix case.
I am grateful to Sh. Saakyan for his interest in this work and lively discussion.
Received: December 8, 2006. Accepted: December 30, 2006. 相似文献
18.
Marco Romito 《Monatshefte für Mathematik》1998,126(4):329-352
Given an open bounded convex subset of
p
, a strictly elliptic differential operatorL and a continuous function
, and denoted withT
L the Dirichlet operator associated withL, the Lototsky-Schnabl operators associated withT
L and are investigated. In particular, conditions are established which ensure the existence of a Feller semigroup represented by limit of powers of these operators. Then the analytic expression of the infinitesimal generator is determined and some properties of the semigroup are deduced. Finally, the saturation class of Lototsky-Schnabl operators is determined.Work supported by a C.N.R. Research Grant (n. 201.19.1, November 30, 1994) 相似文献
19.
Eduardo Hernández Michelle Pierri 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3633-3643
By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. 相似文献
20.
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