Asymptotic Behavior of Non-autonomous Fractional Stochastic p-Laplacian Equations with Delay on $$\mathbb {R}^n$$

2021 ◽  
Author(s):  
Pengyu Chen ◽  
Xiaohui Zhang ◽  
Xuping Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Laplacian Equations ◽  
Equations With Delay

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

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.

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

2020 ◽  
pp. 2050020
Author(s):  
Renhai Wang ◽  
Bixiang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Additive Noise ◽  
Random Coefficients ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Of Solutions ◽  
Additive White Noise ◽  
Approach Zero ◽  
Drift Terms ◽  
Laplacian Equations

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.

scholarly journals Existence and Asymptotic Behavior of Boundary Blow-Up Solutions for Weightedp(x)-Laplacian Equations with Exponential Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-20
Author(s):  
Li Yin ◽  
Yunrui Guo ◽  
Jing Yang ◽  
Bibo Lu ◽  
Qihu Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Blow Up ◽  
Laplacian Equations

This paper investigates the followingp(x)-Laplacian equations with exponential nonlinearities:−Δp(x)u+ρ(x)ef(x,u)=0inΩ,u(x)→+∞asd(x,∂Ω)→0, where−Δp(x)u=−div(|∇u|p(x)−2∇u)is calledp(x)-Laplacian,ρ(x)∈C(Ω). The asymptotic behavior of boundary blow-up solutions is discussed, and the existence of boundary blow-up solutions is given.

scholarly journals Existence of Positive Solutions and Asymptotic Behavior for Evolutionary q(x)-Laplacian Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-23
Author(s):  
Aboubacar Marcos ◽  
Ambroise Soglo
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Variable Exponent ◽  
Probability Space ◽  
Compact Embedding ◽  
Convergence Of Solutions ◽  
Existence Of Positive Solutions ◽  
Wasserstein Space ◽  
Laplacian Equations

In this paper, we extend the variational method of M. Agueh to a large class of parabolic equations involving q(x)-Laplacian parabolic equation ∂ρt,x/∂t=divxρt,x∇xG′ρ+Vqx−2∇xG′ρ+V. The potential V is not necessarily smooth but belongs to a Sobolev space W1,∞Ω. Given the initial datum ρ0 as a probability density on Ω, we use a descent algorithm in the probability space to discretize the q(x)-Laplacian parabolic equation in time. Then, we use compact embedding W1,q.Ω↪↪Lq.Ω established by Fan and Zhao to study the convergence of our algorithm to a weak solution of the q(x)-Laplacian parabolic equation. Finally, we establish the convergence of solutions of the q(x)-Laplacian parabolic equation to equilibrium in the p(.)-variable exponent Wasserstein space.

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