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Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks
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Vojkan Jakšić Vahagn Nersesyan Claude‐Alain Pillet Armen Shirikyan 《纯数学与应用数学通讯》2015,68(12):2108-2143
We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc. 相似文献
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We investigate the existence and stability of standing and travelling multi-hump waves in partial differential equations with reflection and phase symmetries. We focus on 2- and 3-pulse solutions that arise near bi-foci and apply our results to the complex cubic-quintic Ginzburg-Landau equation. 相似文献
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Vahagn Aslanyan 《Archive for Mathematical Logic》2018,57(5-6):629-648
We generalise the exponential Ax–Schanuel theorem to arbitrary linear differential equations with constant coefficients. Using the analysis of the exponential differential equation by Kirby (The theory of exponential differential equations, 2006, Sel Math 15(3):445–486, 2009) and Crampin (Reducts of differentially closed fields to fields with a relation for exponentiation, 2006) we give a complete axiomatisation of the first order theories of linear differential equations and show that the generalised Ax–Schanuel inequalities are adequate for them. 相似文献
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Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications
We prove that the Schrödinger equation is approximately controllable in Sobolev spaces Hs, s>0, generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere S in L2. 相似文献
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We consider a quantum particle in a 1d interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with respect to the control), we prove global exact controllability in a suitable space for arbitrary potential and arbitrary dipole moment. This term is relevant both from the mathematical and physical points of view. The proof uses tools from the bilinear setting and a perturbation argument. 相似文献
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A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables. 相似文献
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Some subnormal embeddings of groups into groups with additionalproperties are established, and in particular, embeddings ofcountable groups into two-generated groups with some extra properties.The results obtained are generalizations of theorems of P. Hall,R. Dark, B. Neumann, H. Neumann and G. Higman on embeddingsof that type. Through the consideration of subnormal embeddingsof finite groups into finite groups with additional properties,a result of H. Heineken and J. Lennox is illustrated. 相似文献
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In this paper, we study the problem of controllability of Schrödinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions. We show also that the system is not exactly controllable in finite time in lower Sobolev spaces. 相似文献