Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping

Li, Fushan; Chen, Zhao

doi:10.1016/j.na.2011.02.033

Cited by 31 publications

(17 citation statements)

References 21 publications

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“…For simple experiments, we only test the discrete data in Movielens dataset without testing other data types popular in the big data environment, e.g., continuous data type [25][26][27][28][29], Boolean data type [30], and fuzzy data type [31][32][33]. In addition, we only test a single criterion (user rating) without discussing the popular cases with multiple criteria [34][35][36][37][38][39][40][41][42][43][44] and their inner linear correlations [45][46][47][48], nonlinear correlations [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66], and weights [67][68][69][70][71][72]…”

Section: Discussionmentioning

confidence: 99%

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

Chen

Yang

2019

J Wireless Com Network

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Recommender systems have become a popular and effective way to quickly discover new service items that are probably preferred by prospective users. Through analyzing the historical service usage data produced in the past, a recommender system can infer the potential user preferences and make accurate recommendations accordingly. However, in the edge environment, the service usage data stored in each edge server are often very sparse, which may result in expected cold-start problems. Besides, in the edge environment, the data required to make an optimal service recommendation decision are often stored in different edge clients or servers, which require additional privacy-preservation strategies to secure the sensitive data involved. Considering the above two drawbacks, traditional locality-sensitive hashing (LSH) is improved to be multi-probing LSH and then introduced to aid the recommendation process so as to guarantee the security and robustness of recommender systems. Experiments conducted on well-known dataset prove the effectiveness and efficiency of the work.

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Section: Discussionmentioning

confidence: 99%

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

Chen

Yang

2019

J Wireless Com Network

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“…Li et al [13][14][15] proved the existence uniqueness, uniform energy decay rates, and limit behavior of the solution to the nonlinear viscoelastic Marguerre-von Kármán shallow shells system. The global existence uniqueness and decay estimates for nonlinear viscoelastic equation with boundary dissipation were given in [16,17,19,[22][23][24][25]. The authors in [10,18,20,21] studied the blowup phenomenon for some evolution equations.…”

Section: Introductionmentioning

confidence: 99%

Global existence and stability of a class of nonlinear evolution equations with hereditary memory and variable density

Jia

2019

Bound Value Probl

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In this paper, we consider the initial boundary value problem of nonlinear evolution equation with hereditary memory, variable density, and external force termUnder suitable assumptions, we prove the existence of a global solution by means of the Galerkin method, establish the exponential stability result by using only one simple auxiliary functional, and give the polynomial stability result. MSC: 35L05; 35L15; 35L70

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“…We mention some other works concerning semilinear wave equations with memory. On the asymptotic behavior of solutions (in the sense of global attractors) see [9,10,13,27,28,29], and on rates of decay of solutions one can also see [24,30,31].…”

Section: Introductionmentioning

confidence: 99%

Regular Global Attractors for Wave Equations with Degenerate Memory

Shomberg

2019

UMJ

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We consider the wave equation with degenerate viscoelastic dissipation recently examined in Cavalcanti, Fatori, and Ma, Attractors for wave equations with degenerate memory, J. Differential Equations (2016). Under certain extra assumptions (namely on the nonlinear term), we show the existence of a compact attracting set which provides further regularity for the global attractor and show that it consists of regular solutions.

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Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping

Cited by 31 publications

References 21 publications

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

Improved LSH for privacy-aware and robust recommender system with sparse data in edge environment

Global existence and stability of a class of nonlinear evolution equations with hereditary memory and variable density

Regular Global Attractors for Wave Equations with Degenerate Memory

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