A singular fractional Kelvin–Voigt model involving a nonlinear operator and their convergence properties

By Jianxin He, Xinguang Zhang, Lishan Liu, Yonghong Wu, Yujun Cui. Boundary Value Problems, 2019

47 citations recorded by the source corpus.

In this paper, we focus on a generalized singular fractional order Kelvin–Voigt model with a nonlinear operator. By using analytic techniques, the uniqueness of solution and an iterative scheme converging to the unique solution are established, which are very helpful to govern the process of the Kelvin–Voigt model. At the same time, the corresponding eigenvalue problem is studied and the property of solution for the eigenvalue problem is established. Some examples are given to illuminate the main results.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/24c16a94a37a7c06c074130120f5bc8ea2440826

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In Applied Mathematics

1. Yujun Cui
2. Xinguang Zhang
3. Lishan Liu
4. Yonghong Wu

In Modeling and Simulation

1. Yujun Cui
2. Xinguang Zhang
3. Lishan Liu
4. Yonghong Wu

In Numerical Analysis

1. Yujun Cui
2. Lishan Liu
3. Yonghong Wu
4. Xinguang Zhang

Citations in the corpus

• A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator (2020, background): “Normally, a blow-up behaviour is often caused by singularity [12,16,20,24,26,27,59,87] and impulse behavior of nonlinearities [4–6,8,10,21,30,34, 44,45,52,53,56,63–65,90,91] in various complex process, but here blow-up phenomena refers to the boundary blow of solution; for more details, see [75, 77,”