共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we study the initial-boundary value problem for infinitely degenerate semilinear parabolic equations with logarithmic nonlinearity , where is an infinitely degenerate system of vector fields, and is an infinitely degenerate elliptic operator. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the logarithmic Sobolev inequality, we obtain the global existence and blow-up at +∞ of solutions with low initial energy or critical initial energy, and we also discuss the asymptotic behavior of the solutions. 相似文献
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Irmina Czarna José-Luis Pérez Tomasz Rolski Kazutoshi Yamazaki 《Stochastic Processes and their Applications》2019,129(12):5406-5449
A level-dependent Lévy process solves the stochastic differential equation , where is a spectrally negative Lévy process. A special case is a multi-refracted Lévy process with . A general rate function that is non-decreasing and locally Lipschitz continuous is also considered. We discuss solutions of the above stochastic differential equation and investigate the so-called scale functions, which are counterparts of the scale functions from the theory of Lévy processes. We show how fluctuation identities for can be expressed via these scale functions. We demonstrate that the derivatives of the scale functions are solutions of Volterra integral equations. 相似文献
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A new criterion for the existence of positive solutions of the second-order delayed differential equation , is given with applications to linear equations. Open problems for future research are formulated. 相似文献
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Abraham Rueda Zoca 《Journal of Mathematical Analysis and Applications》2022,505(1):125447
We study the presence of L-orthogonal elements in connection with Daugavet centers and narrow operators. We prove that if and is a Daugavet center with separable range then, for every non-empty -open subset W of , it follows that contains some L-orthogonal to Y. In the context of narrow operators, we show that if X is separable and is a narrow operator, then given and any non-empty -open subset W of then W contains some L-orthogonal u so that . In the particular case that is separable, we extend the previous result to . Finally, we prove that none of the previous results holds in larger density characters (in particular, a counterexample is shown for under the assumption ). 相似文献
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《Discrete Mathematics》2020,343(2):111658
A well known result in the analysis of finite metric spaces due to Gromov says that given any metric space there exists a tree metric on such that is bounded above by twice . Here is the hyperbolicity of , a quantity that measures the treeness of 4-tuples of points in . This bound is known to be asymptotically tight.We improve this bound by restricting ourselves to metric spaces arising from filtered posets. By doing so we are able to replace the cardinality appearing in Gromov’s bound by a certain poset theoretic invariant which can be much smaller thus significantly improving the approximation bound.The setting of metric spaces arising from posets is rich: For example, every finite metric graph can be induced from a filtered poset. Since every finite metric space can be isometrically embedded into a finite metric graph, our ideas are applicable to finite metric spaces as well.At the core of our results lies the adaptation of the Reeb graph and Reeb tree constructions and the concept of hyperbolicity to the setting of posets, which we use to formulate and prove a tree approximation result for any filtered poset. 相似文献
8.
Émeline Schmisser 《Stochastic Processes and their Applications》2019,129(12):5364-5405
In this article, we consider a jump diffusion process , with drift function , diffusion coefficient and jump coefficient . This process is observed at discrete times . The sampling interval tends to 0 and the time interval tends to infinity. We assume that is ergodic, strictly stationary and exponentially -mixing. We use a penalized least-square approach to compute adaptive estimators of the functions and . We provide bounds for the risks of the two estimators. 相似文献
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The purpose of this paper is to study the second-order nonlinear noncanonical differential equation under the condition . Contrary to most existing results, oscillation of the studied equation is attained via only one condition. We consider both delay and advanced differential equations. A particular example of Euler type equation is provided in order to illustrate the significance of our main results. 相似文献
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Let denote a Hermite process of order and self-similarity parameter . This process is -self-similar, has stationary increments and exhibits long-range dependence. When , it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as . In this paper, we deal with a Vasicek-type model driven by , of the form . Here, and are considered as unknown drift parameters. We provide estimators for and based on continuous-time observations. For all possible values of and , we prove strong consistency and we analyze the asymptotic fluctuations. 相似文献
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We consider a reaction–diffusion–advection equation of the form: for , where is a -periodic function, is a -periodic Fisher–KPP type of nonlinearity with changing sign, is a free boundary satisfying the Stefan condition. We study the long time behavior of solutions and find that there are two critical numbers and with , and , such that a vanishing–spreading dichotomy result holds when ; a vanishing–transition–virtual spreading trichotomy result holds when ; all solutions vanish when or . 相似文献
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The purpose of this study is to derive Hyers–Ulam stability of the linear differential equation without the assumption of continuity of . The obtained result is applied to a control system. 相似文献
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This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity in a bounded domain . We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique. 相似文献
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《Journal of Pure and Applied Algebra》2023,227(2):107190
Let W be a finite Coxeter group and X a subset of W. The length polynomial is defined by , where ? is the length function on W. If then we call the involution length polynomial of W. In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, and the involution length polynomial, in any finite Coxeter group W. In particular, these results correct errors in [11] for the involution length polynomials of Coxeter groups of type and . Moreover, we give a counterexample to a unimodality conjecture stated in [11]. 相似文献
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A.S. Üstünel 《Journal of Functional Analysis》2019,276(11):3468-3483
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Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
18.
Two classes of multivariate random fields with operator-stable marginals are constructed. The random fields with values in are invariant in law under operator-scaling in both the time-domain and the state-space. The construction is based on operator-stable random measures utilizing certain homogeneous functions. 相似文献
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Jean Bertoin 《Stochastic Processes and their Applications》2019,129(4):1443-1454
This work concerns the Ornstein–Uhlenbeck type process associated to a positive self-similar Markov process which drifts to , namely . We point out that is always a (topologically) recurrent ergodic Markov process. We identify its invariant measure in terms of the law of the exponential functional , where is the dual of the real-valued Lévy process related to by the Lamperti transformation. This invariant measure is infinite (i.e. is null-recurrent) if and only if . In that case, we determine the family of Lévy processes for which fulfills the conclusions of the Darling–Kac theorem. Our approach relies crucially on a remarkable connection due to Patie (Patie, 2008) with another generalized Ornstein–Uhlenbeck process that can be associated to the Lévy process , and properties of time-substitutions based on additive functionals. 相似文献