带记忆项非经典扩散方程整体强解的存在性
Existence of Global Strong Solutions for Nonclassical Diffusion Equations with Memory
摘要: 本文主要讨论在强拓扑空间具有衰退记忆的非经典扩散方程解的存在性、唯一性和解对初值的连续依赖性。值得注意的是非线性项满足任意阶多项式指数增长条件。
Abstract: This paper mainly discusses the existence, uniqueness and continuous dependence of a nonclassical diffusion equation with fading memory on . It is worth mentioning that the nonlinearity satisfies the exponential growth conditions of an arbitrary order polynomial.
文章引用：罗双利, 张江卫, 李亚楠. 带记忆项非经典扩散方程整体强解的存在性[J]. 应用数学进展, 2018, 7(10): 1233-1240. https://doi.org/10.12677/AAM.2018.710143

参考文献

[1] Borini, S. and Pata, V. (1999) Uniform Attractors for a Strongly Damped Wave Equation with Linear Memory. Asymptotic Analysis, 20, 263-277.
[2] Conti, M. and Marchini, E.M. (2016) A Remark on Nonclassical Diffusion Equations with Memory. Applied Mathematics and Optimization, 73, 1-21. [Google Scholar] [CrossRef] 
[3] Dafermos, C.M. (1970) Asymptotic Stability in Viscoelasticity. Archive for Rational Mechanics and Analysis, 37, 297-308. [Google Scholar] [CrossRef] 
[4] Grasselli, M. and Pata, V. (2002) Uniform Attractors of Nonautonomous Systems with Memory. In: Lorenzi, A. and Ruf, B., Eds., Evolution Equations, Semigroups and Functional Analysis, Springer, Berlin, 155-178
[5] Barenblatt, G.I., Zheltov, I.P. and Kochina, I.N. (1960) Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks. Journal of Applied Mathematics and Mechanics, 24, 1286-1303. [Google Scholar] [CrossRef] 
[6] Chen, P.J. and Gurtin, M.E. (1968) On a Theory of Heat Conduction Involving Two Temperatures. Zeitschrift fur Angewandte Mathematik und Physik, 19, 614-627. [Google Scholar] [CrossRef] 
[7] Jackle, J. (1990) Heat Conduction and Relaxation in Liquids of High Viscosity. Physica A, 162, 377-404. [Google Scholar] [CrossRef] 
[8] Aifantis, E.C. (1980) On the Problem of Diffusion in Solids. Acta Mechanica, 37, 265-296. [Google Scholar] [CrossRef] 
[9] Wang, X., Yang, L. and Zhong, C. (2010) Attractors for the Nonclassical Diffusion Equations with Fading Memory. Journal of Mathematical Analysis and Applications, 362, 327-337. [Google Scholar] [CrossRef] 
[10] Anh, C.T., Phuong Thanh, D.T. and Toan, N.D. (2017) Global Attractors for Nonclassical Diffusion Equations with Hereditary Memory and a New Class of Nonlinearities. Annales Polonici Mathematici, 119, 1-21. [Google Scholar] [CrossRef] 
[11] Xie, Y., Li, Q. and Zhu, K. (2016) Attractors for Nonclassical Diffusion Equations with Arbitrary Polynomial Growth Nonlinearity. Nonlinear Analysis: Real World Applications, 31, 23-37. [Google Scholar] [CrossRef] 
[12] Evans L.C.M. (1998) Partial Differential Equation: GSM. American Mathematical Society, Rhode Island.

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