共查询到20条相似文献,搜索用时 22 毫秒
1.
We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection–reaction–diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c? such that for each wave speed c≤c?, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c≤c? are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves with speed c>c?. 相似文献
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Let E be a Banach lattice and F a Banach space. A bounded linear operator T:E→F is an isomorphism on the positive cone of E if and only if T∗ is almost surjective. A dual version of this theorem holds also. A bounded linear operator T:F→E is almost surjective if and only if T∗ is an isomorphism on the positive cone of F∗. 相似文献
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Michel Mandjes Petteri Mannersalo Ilkka Norros Miranda van Uitert 《Stochastic Processes and their Applications》2006
Consider events of the form {Zs≥ζ(s),s∈S}, where Z is a continuous Gaussian process with stationary increments, ζ is a function that belongs to the reproducing kernel Hilbert space R of process Z, and S⊂R is compact. The main problem considered in this paper is identifying the function β∗∈R satisfying β∗(s)≥ζ(s) on S and having minimal R-norm. The smoothness (mean square differentiability) of Z turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s for s∈[0,1] and Z is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process. 相似文献
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The paper deals with the radially symmetric solutions of ut=Δu+um(x,t)vn(0,t), vt=Δv+up(0,t)vq(x,t), subject to null Dirichlet boundary conditions. For the blow-up classical solutions, we propose the critical exponents for non-simultaneous blow-up by determining the complete and optimal classification for all the non-negative exponents: (i) There exist initial data such that u (v) blows up alone if and only if m>p+1 (q>n+1), which means that any blow-up is simultaneous if and only if m≤p+1, q≤n+1. (ii) Any blow-up is u (v) blowing up with v (u) remaining bounded if and only if m>p+1, q≤n+1 (m≤p+1, q>n+1). (iii) Both non-simultaneous and simultaneous blow-up may occur if and only if m>p+1, q>n+1. Moreover, we consider the blow-up rate and set estimates which were not obtained in the previously known work for the same model. 相似文献
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We show that if T:X→X is a continuous linear operator on an F-space X≠{0}, then the set of frequently hypercyclic vectors of T is of first category in X, and this answers a question of A. Bonilla and K.-G. Grosse-Erdmann. We also show that if T:X→X is a bounded linear operator on a Banach space X≠{0} and if T is frequently hypercyclic (or, more generally, syndetically transitive), then the T∗-orbit of every non-zero element of X∗ is bounded away from 0, and in particular T∗ is not hypercyclic. 相似文献
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Tertuliano Franco Patrícia Gonçalves Adriana Neumann 《Stochastic Processes and their Applications》2013
We analyze the equilibrium fluctuations of density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is αn−β, with α>0, β∈[0,+∞] and n is the scaling parameter. Depending on the regime of β, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value β=1, starting a tagged particle near the slow bond, we obtain a family of Gaussian processes indexed in α, interpolating a fractional Brownian motion of Hurst exponent 1/4 and the degenerate process equal to zero. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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We investigate the asymptotic speed of propagation and monotone traveling wave solutions for a lattice integral equation which is an epidemic model while the population is distributed on one-dimensional lattice Z. It is proved that the asymptotic speed of propagation c∗ coincides with the minimal wave speed. 相似文献
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We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces, and we define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and cone-to-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (in the classical sense) and K-monotone functions defined by Borwein, Burke and Lewis to mappings with domains and ranges of higher dimensions. First, using results of Veselý and Zají?ek, we show some relationships between these classes. Then, we show that every K-monotone function f:X→R, where X is any Banach space, is continuous outside of a set which can be covered by countably many Lipschitz hypersurfaces. This sharpens a result due to Borwein and Wang. As a consequence, we obtain a similar result for K-monotone dominated and cone-to-cone monotone mappings. Finally, we prove several results concerning almost everywhere differentiability (also in metric and w∗-senses) of these mappings. 相似文献
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We prove that θ∗ as previously defined [Int. J. Contemp. Math. Sci. 5 (2010) 721] is the smallest equivalence relation such that the quotient structure R/θ∗ is a commutative fundamental ring. We also investigate some properties with respect to the commutative fundamental relation θ∗ on a hyperring R. 相似文献
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By a perturbation method and constructing comparison functions, we reveal how the inhomogeneous term h affects the exact asymptotic behaviour of solutions near the boundary to the problem △u=b(x)g(u)+λh(x), u>0 in Ω, u|∂Ω=∞, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1[0,∞) is increasing on [0,∞), g(0)=0, g′ is regularly varying at infinity with positive index ρ, the weight b, which is non-trivial and non-negative in Ω, may be vanishing on the boundary, and the inhomogeneous term h is non-negative in Ω and may be singular on the boundary. 相似文献
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Radu Ioan Boţ Ernö Robert Csetnek Gert Wanka 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper we give a weaker sufficient condition for the maximal monotonicity of the operator S+A∗TA, where S:X?X∗, T:Y?Y∗ are two maximal monotone operators, A:X→Y is a linear continuous mapping and X,Y are reflexive Banach spaces. We prove that our condition is weaker than the generalized interior-point conditions given so far in the literature. This condition is formulated using the representative functions of the operators involved. In particular, we rediscover some sufficient conditions given in the past using the so-called Fitzpatrick function for the maximal monotonicity of the sum of two maximal monotone operators and for the precomposition of a maximal monotone operator with a linear operator, respectively. 相似文献
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In the Hammersley harness processes the R-valued height at each site i∈Zd is updated at rate 1 to an average of the neighboring heights plus a centered random variable (the noise). We construct the process “a la Harris” simultaneously for all times and boxes contained in Zd. With this representation we compute covariances and show L2 and almost sure time and space convergence of the process. In particular, the process started from the flat configuration and viewed from the height at the origin converges to an invariant measure. In dimension three and higher, the process itself converges to an invariant measure in L2 at speed t1−d/2 (this extends the convergence established by Hsiao). When the noise is Gaussian the limiting measures are Gaussian fields (harmonic crystals) and are also reversible for the process. 相似文献
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In this paper, a nonautonomous SIRS epidemic model with time delay is studied. We introduce some new threshold values R∗ and R∗ and further obtain the disease will be permanent when R∗>1 and the disease extinct when R∗<1. Using the method of Liapunov functional, some sufficient conditions are derived for the global attractivity of the system. The known results are extended. 相似文献
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It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established. 相似文献