一类偏泛函微分方程的测度伪型解及在生物数学模型中的应用
A Class of Measure Pseudo Type Solution of Partial Functional Differential Equations and Applications in Biomathematical Model
摘要: 本文研究了一类具有无限时滞的α-型偏泛函微分方程测度伪型解的存在性和唯一性。 文中假设线 性算子部分在Banach 空间X 上生成紧的解析半群，然后利用分数幕算子理论和算子半群理论证明了方程解的存在唯一性，并将其应用于一类生物数学模型中，验证结论的正确性。
Abstract: In this paper, the existence, uniqueness of measure pseudo type solutions in the α-form for partial functional differential equations with infinite delay are investigated. Here we assume that the linear part generates a compact analytic semigroup on a Banach space X, the delayed part is assumed to be continuous with respect to the fractional power of the generator. Finally, an example of biomathematical model is presented to illustrate the main findings.
文章引用：王芳. 一类偏泛函微分方程的测度伪型解及在生物数学模型中的应用[J]. 应用数学进展, 2023, 12(5): 2480-2492. https://doi.org/10.12677/AAM.2023.125250

参考文献

[1] Adimy, M., Ezzinbi, K. and Ouhinou, A. (2006) Variation of Constants Formula and Almost Periodic Solutions for Some Partial Functional Differential Equations with Infinite Delay. Jour- nal of Mathematical Analysis and Applications, 317, 668-689. [Google Scholar] [CrossRef] 
[2] Elazzouzi, A. and Ouhinou, A. (2010) Variation of Constants Formula and Reduction Principle for a Class of Partial Functional Differential Equations with Infinite Delay. Nonlinear Analysis, 73, 1980-2000. [Google Scholar] [CrossRef] 
[3] Ezzinbi, K., Kyelem, B.A. and Ouaro, S. (2014) Periodicity in the α-Norm for Partial Func- tional Differential Equations in Fading Memory Spaces. Nonlinear Analysis, 97, 30-54. [Google Scholar] [CrossRef] 
[4] Adimy, M., Ezzinbi, K. and Marquet, C. (2014) Ergodic and Weighted Pseudo-Almost Periodic Solutions for Partial Functional Differential Equations in Fading Memory Spaces. Journal of Applied Mathematics and Computing, 44, 147-165. [Google Scholar] [CrossRef] 
[5] Ezzinbi, K., Fatajou, S. and N’Gu´er´ekata, G.M. (2008) Massera-Type Theorem for the Ex- istence of C(n)-Almost-Periodic Solutions for Partial Functional Differential Equations with Infinite Delay. Nonlinear Analysis, 69, 1413-1424. [Google Scholar] [CrossRef] 
[6] Ezzinbi, K. and Zabsonre, I. (2013) Pseudo Almost Periodic Solutions of Infinite Class for Some Functional Differential Equations. Applicable Analysis, 92, 1627-1642.
https://doi.org/ 10.1080/00036811.2012.698003
[7] Ezzinbi, K., Fatajou, S. and N’Gu´er´ekata, G.M. (2008) Pseudo Almost Automorphic Solutions for Some Partial Functional Differential Equations with Infinite Delay. Applicable Analysis, 87, 591-605. [Google Scholar] [CrossRef] 
[8] Ezzinbi, K. and N’Gu´er´ekata, G.M. (2007) Almost Automorphic Solutions for Partial Func- tional Differential Equations with Infinite Delay. Semigroup Forum, 75, 95-115. [Google Scholar] [CrossRef] 
[9] Ezzinbi, K. and Miraoui, M. (2015) µ-Pseudo Almost Periodic and Automorphic Solutions in the α-Norm for Some Partial Functional Differential Equations. Numerical Functional Analysis and Optimization, 36, 991-1012. [Google Scholar] [CrossRef] 
[10] Ezzinbi, K., Miraoui, M. and Rebey, A. (2016) Measure Pseudo-Almost Periodic Solutions in the α-Norm to Some Neutral Partial Differential Equations with Delay. Mediterranean Journal of Mathematics, 13, 3417-3431. [Google Scholar] [CrossRef] 
[11] Bouzahir, H. (2006) Existence and Regularity of Local Solutions to Partial Neutral Functional Differential Equations with Infinite Delay. Electronic Journal of Differential Equations, 2006, Paper No. 88.
[12] Elazzouzi, A. and Ouhinou, A. (2011) Optimal Regularity and Stability Analysis in the α- Norm for a Class of Partial Functional Differential Equations with Infinite Delay. Discrete and Continuous Dynamical Systems, 30, 115-135. [Google Scholar] [CrossRef] 
[13] Ezzinbi, K., Ghnimi, S. and Taoudi, M.A. (2010) Existence and Regularity of Solutions for Neutral Partial Functional Integrodifferential Equations with Infinite Delay. Nonlinear Analy- sis: Hybrid Systems, 4, 54-64. [Google Scholar] [CrossRef] 
[14] Adimy, M., Bouzahir, H. and Ezzinbi, K. (2004) Existence and Stability for Some Partial Neu- tral Functional Differential Equations with Infinite Delay. Journal of Mathematical Analysis and Applications, 294, 438-461. [Google Scholar] [CrossRef] 
[15] Benkhalti, R. and Ezzinbi, K. (2006) Existence and Stability in the α-Norm for Some Partial Functional Differential Equations with Infinite Delay. Differential and Integral Equations, 19, 545-572. [Google Scholar] [CrossRef] 
[16] Hale, J. and Kato, J. (1978) Phase Space for Retarded Equations with Unbounded Delay. Funkcialaj Ekvacioj, 21, 11-41.
[17] Hasler, M.F. and N’Gu´er´ekata, G.M. (2014) Bloch-Periodic Functions and Some Applications. Nonlinear Studies, 21, 21-30.
[18] Wang, J.L. and Li, H.F. (2006) The Weighted Periodic Function and Its Properties. Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 13, 1179- 1183.
[19] Fink, A.M. (1974) Almost Periodic Differential Equations. Springer, New York. [Google Scholar] [CrossRef] 
[20] Bochner, S. (1962) A New Approach to Almost Periodicity. Proceedings of the National Acade- my of Sciences of the United States of America, 48, 2039-2043. [Google Scholar] [CrossRef] [PubMed]
[21] Diagana, T., Ezzinbi, K. and Miraoui, M. (2014) Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory. Cubo, 16, 1-31. [Google Scholar] [CrossRef] 
[22] Pazy, A. (1983) Semigroup of Linear Operators and Applications to Partial Differential Equa- tions, Springer-Verlag, New York. [Google Scholar] [CrossRef] 
[23] Hino, Y., Murakami, S. and Naito, T. (1991) Functional Differential Equations with Unbound- ed Delay. In: Lectures Notes, Vol. 1473, Springer Berlin, Heidelberg. [Google Scholar] [CrossRef] 
[24] Adimy, M., Elazzouzi, A. and Ezzinbi, K. (2009) Reduction Principle and Dynamic Behaviors for a Class of Partial Functional Differential Equations. Nonlinear Analysis, 71, 1709-1727. [Google Scholar] [CrossRef] 
[25] Blot, J., Cieutat, P. and Ezzinbi, K. (2013) New Approach for Weighted Pseudo-Almost Peri- odic Functions under the Light of Measure Theory, Basic Results and Applications. Applicable Analysis, 92, 493-526. [Google Scholar] [CrossRef] 

为你推荐