Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains

This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic [Formula: see text]-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain [Formula: see text]. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in [Formula: see text]. This attractor is further proved to be a bi-spatial [Formula: see text]-attractor for any [Formula: see text], which is compact, measurable in [Formula: see text] and attracts all random subsets of [Formula: see text] with respect to the norm of [Formula: see text]. Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in [Formula: see text] for [Formula: see text] in order to overcome the non-compactness of Sobolev embeddings on [Formula: see text] and the nonlinearity of the fractional [Formula: see text]-Laplace operator.

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Dynamics of stochastic FitzHugh–Nagumo systems with additive noise on unbounded thin domains

Stochastics and Dynamics ◽

10.1142/s0219493720500185 ◽

2019 ◽

Vol 20 (03) ◽

pp. 2050018

Author(s):

Lin Shi ◽

Dingshi Li ◽

Xiliang Li ◽

Xiaohu Wang

Keyword(s):

Asymptotic Behavior ◽

White Noise ◽

Unbounded Domain ◽

Existence And Uniqueness ◽

Additive Noise ◽

Upper Semicontinuity ◽

Thin Domains ◽

Additive White Noise ◽

Random Attractors ◽

Lower Dimensional

We investigate the asymptotic behavior of a class of non-autonomous stochastic FitzHugh–Nagumo systems driven by additive white noise on unbounded thin domains. For this aim, we first show the existence and uniqueness of random attractors for the considered equations and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.

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Asymptotic behavior of solutions for a semibounded nonmonotone evolution equation

Abstract and Applied Analysis ◽

10.1155/s1085337503210022 ◽

2003 ◽

Vol 2003 (9) ◽

pp. 521-538

Author(s):

Nikos Karachalios ◽

Nikos Stavrakakis ◽

Pavlos Xanthopoulos

Keyword(s):

Dynamical System ◽

Asymptotic Behavior ◽

Parabolic Equation ◽

Evolution Equation ◽

Existence And Uniqueness ◽

Nonlinear Parabolic Equation ◽

Evolution Equations ◽

Asymptotic Behavior Of Solutions ◽

Uniqueness Of Solutions ◽

Nonlinear Parabolic

We consider a nonlinear parabolic equation involving nonmonotone diffusion. Existence and uniqueness of solutions are obtained, employing methods for semibounded evolution equations. Also shown is the existence of a global attractor for the corresponding dynamical system.

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Asymptotic Behavior of the Solutions of the Generalized Globally Modified Navier–Stokes Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2021/9924912 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Yonghong Duan ◽

Xiaojuan Chai

Keyword(s):

Asymptotic Behavior ◽

Existence And Uniqueness ◽

Stokes Equations ◽

Global Attractors ◽

Navier Stokes ◽

Asymptotic Behavior Of Solutions ◽

Uniqueness Of Solutions ◽

Navier Stokes Equations

The paper is concerned with the existence and the asymptotic behavior of solutions to a class of generalized Navier–Stokes equations, which generalises the so-called globally modified Navier–Stokes equations. The existence and uniqueness of solutions are proved under different assumptions on the dissipation and modification factors. For the asymptotic behavior of solutions, we prove the existence of global attractors in proper spaces. The results generalize some results derived in our previous work Ann. Polon. Math. 122(2):101–128(2019).

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Long Term Behavior for a Class of Stochastic Delay Lattice Systems in Xρ Space

Discrete Dynamics in Nature and Society ◽

10.1155/2020/5405947 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

Yijin Zhang ◽

Zongbing Lin

Keyword(s):

Dynamical System ◽

Asymptotic Behavior ◽

Existence And Uniqueness ◽

Additive Noise ◽

Asymptotic Behavior Of Solutions ◽

Random Dynamical System ◽

Lattice Systems ◽

Stochastic Delay ◽

Long Term Behavior

In this paper, we focus on the asymptotic behavior of solutions to stochastic delay lattice equations with additive noise and deterministic forcing. We first show the existence of a continuous random dynamical system for the equations. Then we investigate the pullback asymptotical compactness of solutions as well as the existence and uniqueness of tempered random attractor in Xρ space. Finally, ergodicity of the systems is achieved.

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An asymptotic analysis for Hamilton–Jacobi equations with large Hamiltonian drift terms

Advances in Calculus of Variations ◽

10.1515/acv-2017-0046 ◽

2017 ◽

Vol 0 (0) ◽

Author(s):

Taiga Kumagai

Keyword(s):

Asymptotic Behavior ◽

Euclidean Space ◽

Asymptotic Analysis ◽

Open Subset ◽

Dimensional Euclidean Space ◽

Asymptotic Behavior Of Solutions ◽

Two Dimensional ◽

Jacobi Equations ◽

Drift Terms

AbstractWe investigate the asymptotic behavior of solutions of Hamilton–Jacobi equations with large Hamiltonian drift terms in an open subset of the two-dimensional Euclidean space. The drift is given by

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Asymptotic behavior for non-autonomous stochastic plate equation on unbounded domains

Open Mathematics ◽

10.1515/math-2019-0092 ◽

2019 ◽

Vol 17 (1) ◽

pp. 1281-1302 ◽

Cited By ~ 2

Author(s):

Xiaobin Yao ◽

Xilan Liu

Keyword(s):

Asymptotic Behavior ◽

Additive Noise ◽

Upper Semicontinuity ◽

Unbounded Domains ◽

Asymptotic Behavior Of Solutions ◽

Plate Equation ◽

Uniform Estimates ◽

Estimates Of Solutions ◽

Random Attractors

Abstract We study the asymptotic behavior of solutions to the non-autonomous stochastic plate equation driven by additive noise defined on unbounded domains. We first prove the uniform estimates of solutions, and then establish the existence and upper semicontinuity of random attractors.

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Modeling and analysis of adipocytes dynamic with a differentiation process

ESAIM Proceedings and Surveys ◽

10.1051/proc/202067013 ◽

2020 ◽

Vol 67 ◽

pp. 210-241

Author(s):

Jérôme Gilleron ◽

Thierry Goudon ◽

Frédéric Lagoutière ◽

Hugo Martin ◽

Benjamin Mauroy ◽

...

Keyword(s):

Experimental Data ◽

Growth Rate ◽

Existence And Uniqueness ◽

Stationary Solutions ◽

Asymptotic Behavior Of Solutions ◽

Advection Equation ◽

Differentiation Process ◽

Uniqueness Of Solutions ◽

Modeling And Analysis ◽

The Mean

We propose in this article a model describing the dynamic of a system of adipocytes, structured by their sizes. This model takes into account the differentiation of a population of mesenchymal cells into preadipocytes and of preadipocytes into adipocytes; the differentiation rates depend on the mean adipocyte radius. The considered equations are therefore ordinary differential equations, coupled with an advection equation, the growth rate of which depends on food availability and on the total surface of adipocytes. Since this velocity is discontinuous, we need to introduce a convenient notion of solutions coming from Filippov theory. We are consequently able to determine the stationary solutions of the system, to prove the existence and uniqueness of solutions and to describe the asymptotic behavior of solutions in some simple cases. Finally, the parameters of the model are ﬁtted thanks to some experimental data and numerical simulations are displayed; a spatial extension of the model is studied numerically.

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Prescribed conditions at infinity for fractional parabolic and elliptic equations with unbounded coefficients

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2016077 ◽

2018 ◽

Vol 24 (1) ◽

pp. 105-127

Author(s):

Fabio Punzo ◽

Enrico Valdinoci

Keyword(s):

Asymptotic Behavior ◽

Parabolic Equations ◽

Elliptic Equations ◽

Existence And Uniqueness ◽

Time Dependent ◽

Uniqueness Of Solutions ◽

Unbounded Coefficients ◽

Conditions At Infinity

We investigate existence and uniqueness of solutions to a class of fractional parabolic equations satisfying prescribed point-wise conditions at infinity (in space), which can be time-dependent. Moreover, we study the asymptotic behavior of such solutions. We also consider solutions of elliptic equations satisfying appropriate conditions at infinity.

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RANDOM ATTRACTORS FOR SECOND ORDER STOCHASTIC LATTICE DYNAMICAL SYSTEMS WITH MULTIPLICATIVE NOISE IN WEIGHTED SPACES

Stochastics and Dynamics ◽

10.1142/s0219493711500249 ◽

2012 ◽

Vol 12 (03) ◽

pp. 1150024 ◽

Cited By ~ 16

Author(s):

XIAOYING HAN

Keyword(s):

Existence And Uniqueness ◽

Multiplicative Noise ◽

Sufficient Conditions ◽

Second Order ◽

Weighted Spaces ◽

Asymptotic Behavior Of Solutions ◽

Uniqueness Of Solutions ◽

Absorbing Sets ◽

Random Attractors ◽

Multiplicative White Noise

In this paper, we study the asymptotic behavior of solutions of a second order stochastic lattice differential equation with multiplicative white noise in weighted spaces. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then establish the existence of tempered random bounded absorbing sets and global random attractors.

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Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equations with delay term and variadle exponents

10.22541/au.160975791.14681913/v1 ◽

2021 ◽

Author(s):

Stanilslav Antontsev ◽

Jorge Ferreira ◽

Erhan Pişkin ◽

Hazal Yüksekkaya

Keyword(s):

Asymptotic Behavior ◽

Integral Inequality ◽

Blow Up ◽

Asymptotic Behavior Of Solutions ◽

Variable Exponents ◽

Delay Term ◽

Laplacian Equation ◽

Laplacian Equations ◽

Equation With Delay ◽

Equations With Delay

In this paper, we consider a nonlinear p .x/Laplacian equation with delay of time and variable exponents. Firstly, we prove the blow up of solutions. Then, by applying an integral inequality due to Komornik, we obtain the decay result. These results improve and extend earlier results in the literature.

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