IF 1.2 3区 数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2025-02-18 DOI:10.1016/j.jmaa.2025.129390
Nguyen Nhu Quan
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引用次数: 0

摘要

在这项研究中,我们关注一类由分数布朗运动驱动的非线性负阶希尔伯特尺度取值的反常扩散方程。通过使用分解理论、定点论证和分数 Sobolev 空间的嵌入,我们证明了全局可解性,并给出了一些充分条件,以确保均方矩中温和解的渐近稳定性。
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The existences and asymptotic behavior of solutions to stochastic semilinear anomalous diffusion equations
In this work, we are concerned a class of anomalous diffusion equations with the nonlinearities taking values in Hilbert scales of negative order driven by fractional Brownian motion. By using the resolvent theory, fixed point argument and embeddings of fractional Sobolev spaces we prove the global solvability and give some sufficient conditions to ensure the asymptotic stability of mild solutions in the mean square moment.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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