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991.
Algebraic dichotomies with an application to the stability of Riemann solutions of conservation laws
Xiao-Biao Lin 《Journal of Differential Equations》2009,247(11):2924-2965
Recently, there has been some interest on the stability of waves where the functions involved grow or decay at an algebraic rate m|x|. In this paper we define the so-called algebraic dichotomy that may aid in treating such problems. We discuss the basic properties of the algebraic dichotomy, methods of detecting it, and calculating the power of the weight function.We present several examples: (1) The Bessel equation. (2) The n-degree Fisher type equation. (3) Hyperbolic conservation laws in similarity coordinates. (4) A system of conservation laws with a Dafermos type viscous regularization. We show that the linearized system generates an analytic semigroup in the space of algebraic decay functions. This example motivates our work on algebraic dichotomies. 相似文献
992.
This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(u(x,t)) in the quasi‐linear parabolic equation ut(x,t)=(k(u(x,t))ux(x,t))x, with Dirichlet boundary conditions u(0,t)=ψ0, u(1,t)=ψ1. The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[?]:?? →C1[0,T], Ψ[?]:??→C1[0,T] via semigroup theory. In this paper, it is shown that if the null space of the semigroup T(t) consists of only zero function, then the input–output mappings Φ[?] and Ψ[?] have the distinguishability property. It is also shown that the types of the boundary conditions and the region on which the problem is defined play an important role in the distinguishability property of these mappings. Moreover, under the light of measured output data (boundary observations) f(t):=k(u(0,t))ux(0,t) or/and h(t):=k(u(1,t))ux(1,t), the values k(ψ0) and k(ψ1) of the unknown diffusion coefficient k(u(x,t)) at (x,t)=(0,0) and (x,t)=(1,0), respectively, can be determined explicitly. In addition to these, the values ku(ψ0) and ku(ψ1) of the unknown coefficient k(u(x,t)) at (x,t)=(0,0) and (x,t)=(1,0), respectively, are also determined via the input data. Furthermore, it is shown that measured output data f(t) and h(t) can be determined analytically by an integral representation. Hence the input–output mappings Φ[?]:??→ C1[0,T], Ψ[?]:??→C1[0,T] are given explicitly in terms of the semigroup. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
993.
994.
The concept of pure gaps of a Weierstrass semigroup at several points of an algebraic curve has been used lately to obtain
codes that have a lower bound for the minimum distance which is greater than the Goppa bound. In this work, we show that the
existence of total inflection points on a smooth plane curve determines the existence of pure gaps in certain Weierstrass
semigroups. We then apply our results to the Hermitian curve and construct codes supported on several points that compare
better to one-point codes from that same curve.
相似文献
995.
We develop the perturbation theory for propagators, with the objective to prove Gaussian bounds. Let U be a strongly continuous propagator, i.e., a family of operators describing the solutions of a non-autonomous evolution equation, on an Lp-space, and assume that U is positive and satisfies Gaussian upper and lower bounds. Let V be a (time-dependent) potential satisfying certain Miyadera conditions with respect to U. We show that then the perturbed propagator enjoys Gaussian upper and lower bounds as well. To prepare the necessary tools, we extend the perturbation theory of strongly continuous propagators and the theory of absorption propagators. 相似文献
996.
In this paper, by using a fixed point theorem for condensing multi-valued maps, we have investigated the existence of mild solutions for a class of semilinear impulsive neutral functional differential inclusions with nonlocal conditions. As an application, an example has been presented to illustrate the results obtained. 相似文献
997.
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given. 相似文献
998.
曹六川 《数学物理学报(B辑英文版)》2006,26(2):246-254
This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almost-orbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results. 相似文献
999.
Ebru Ozbilge 《Mathematical Methods in the Applied Sciences》2008,31(11):1333-1344
In this article, a semigroup approach is presented for the mathematical analysis of the inverse coefficient problems of identifying the unknown diffusion coefficient k(u(x, t)) in the quasi‐linear parabolic equation ut(x, t)=(k(u(x, t))ux(x, t))x, with Dirichlet boundary conditions ux(0, t)=ψ0, u(1, t)=ψ1. The main purpose of this work is to analyze the distinguishability of the input–output mappings Φ[·] : ??→C1[0, T], Ψ[·] : ??→C1[0, T] using semigroup theory. In this article, it is shown that if the null space of semigroups T(t) and S(t) consists of only a zero function, then the input–output mappings Φ[·] and Ψ[·] have the distinguishability property. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
1000.
An extension of the Perron-Frobenius Theorem is presented in the much more general setting of indecomposable semigroups of nonnegative matrices. Many features of the original theorem including the existence of a fixed positive vector, a block-monomial form, and spectral stability properties hold simultaneously for these semigroups. The paper is largely self-contained and the proofs are elementary. The classical theorem and some related results follow as corollaries. 相似文献