TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY

doi:10.1016/S0252-9602(13)60033-8

Abstract

CLC Number:

37L05

WANG Yong-Hai, WANG Ling-Zhi. TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY[J].Acta mathematica scientia,Series B, 2013, 33(3): 721-737.

Trendmd

[1] Aifantis E C. On the problem of diffusion in solids. Acta Mech, 1980, 37: 265–296

[2] Borini S, Pata V. Uniform attractors for a strongly damped wave equation with linear memory. Asymptotic Anal, 1999, 20: 263–277

[3] Caraballo T, Chueshov I D, Real J. Pullback attractors for stochastic heat equations in materials with memory. Discrete Cont Dyn Syst Series B, 2008, 9: 525–539

[4] Caraballo T, Garrido–Atienza M J, Schmalfuß B, Valero J. Global attractor for a non–autonomous integro–differential equation in materials with memory. Nonlinear Anal, TMA, 2010, 73: 183–201

[5] Chepyzhov V V, Gatti S, Grasselli M, et al. Trajectory and global attractors for evolution equations with memory. Appl Math Lett, 2006, 19: 87–96

[6] Chepyzhov V V, Mainini E, Pata V. Stability of abstract linear semigroups arising from heat conduction with memory. Asymptotic Analysis, 2006, 50: 269–291

[7] Chepyzhov V V, Miranville A. Trajectory and global attractors of dissipative hyperbolic equations with memory. Commun Pure Appl Anal, 2005, 4: 115–142

[8] Chepyzhov V V, Miranville A. On trajectory and global attractors for semilinear heat equations with fading memory. Indiana University Math J, 2006, 55: 119–167

[9] Chepyzhov V V, Vishik M I. Attractors for equations of mathematical physics. Amer Math Soc Colloq Publ 49. Providence, RI: Amer Math Soc, 2002

[10] Conti M, Pata V, Squassina M. Singular limit of differential systems with memory. Indiana University Math J, 2006, 55: 169–215

[11] Dafermos C M. Asymptotic stability in viscoelasticity. Arch Rational Mech Anal, 1970, 37: 297–308

[12] Giorgi C, Grasselli M, Pata V. Uniform attractors for a phase–field model with memory and quadratic nonlinearity. Indiana Univ Math J, 1999, 48: 1395–1445

[13] Giorgi C, Grasselli M, Pata V.Well–posedness and longtime behavior of the phase–field model with memory
in a history space setting. Quart Appl Math, 2001, 59: 701–736

[14] Giorgi C, Pata V, Marzocchi A. Asymptotic behavior of a semilinear problem in heat conduction with memory. Nonlinear Diff Eq Appl, 1998, 5: 333–354

[15] Grasselli M, Pata V. Upper semicontinuous attractor for a hyperbolic phase–field model with memory. Indiana Univ Math J, 2001, 50: 1281–1308

[16] Kloeden P E, Real J, Sun C Y. Robust exponential attractors for non–autonomous equations with memory. Commun Pure Appl Anal, 2011, 10: 885–915

[17] Lions J L, Magenes E. Non–Homogeneous Boundary Value Problems and Applications. Springer–Verlag, 1972

[18] Pata V. Attractors for a damped wave equation on R3 with linear memory. Math Meth Appl Sci Appl, 2000, 23: 633–653

[19] Pata V, Zucchi A. Attractors for a damped hyperbolic equation with linear memory. Adv Math Sci Appl, 2001, 11: 505–529

[20] Pata V. Hyperbolic limit of parabolic semilinear heat equations with fading memory. Z Anal Anwendungen, 2001, 20: 359–377

[21] Sun C Y, Cao D M, Duan J Q. Non–autonomous wave dynamics with memory–Asymptotic regularity and uniform attractor. Discrete Cont Dyn Syst, 2008, 9B: 743–761

[22] Sun C Y, Wang S Y, Zhong C K. Global attractors for a nonclassical diffusion equation. Acta Mathematica Sinica, English Series, 2007, 23: 1271–1280

[23] Sun C Y, Yang M H. Dynamics of the nonclassical diffusion equations. Asymptotic Anal, 2008, 59: 51–81

[24] Temam R. Infinite–dimensional dynamical systems in mechanics and physics. Springer-Verlag, 1997

[25] Wang X, Zhong C K. Attractors for the non–autonomous nonclassical diffusion equations with fading memory. Nonlinear Anal, 2009, 71: 5733–5746

[26] Wang Y H, Qin Y M. Upper semicontinuity of pullback attractors for nonclassical diffusion equations. J Math Phys, 2010, 51: 022701

[27] Wang S Y, Li D S, Zhong C K. On the dynamics of a class of nonclassical parabolic equations. J Math Anal Appl, 2006, 317: 565–582

[28] Xiao Y L. Attractors for a nonclassical diffusion equation. Acta Mathematicae Applicatae Sinica, English Series, 2002, 18: 273–276

[29] Zhao C D, Jia X L, Yang X B. Uniform attractor for nonautonomous in compressible non-Newtonian fluid with a new class of external force. Acta Mathematica Scientia, 2011, 31B(5): 1803–1812

TRAJECTORY ATTRACTORS FOR NONCLASSICAL DIFFUSION EQUATIONS WITH FADING MEMORY

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 12

Metrics

Comments

Recommended 10

[1]	Azer KHANMAMEDOV, Sema YAYLA. LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N [J]. Acta mathematica scientia,Series B, 2018, 38(3): 1025-1042.
[2]	Lei ZHANG, Bin LIU. THE GLOBAL ATTRACTOR FOR A VISCOUS WEAKLY DISSIPATIVE GENERALIZED TWO-COMPONENT μ-HUNTER-SAXTON SYSTEM [J]. Acta mathematica scientia,Series B, 2018, 38(2): 651-672.
[3]	Chengzhi WANG, Mingshu ZHANG, Caidi ZHAO. EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW [J]. Acta mathematica scientia,Series B, 2018, 38(1): 187-202.
[4]	ZHANG Fa-Yong, GUO Bai-Ling. ATTRACTORS FOR FULLY DISCRETE FINITE DIFFERENCE SCHEME OF DISSIPATIVE ZAKHAROV EQUATIONS [J]. Acta mathematica scientia,Series B, 2012, 32(6): 2431-2452.
[5]	CHEN Xue-Yong, LIU Wei-An. GLOBAL ATTRACTOR FOR A DENSITY-DEPENDENT SENSITIVITY CHEMOTAXIS MODEL [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1365-1375.
[6]	ZHANG Yin-Di, LI Kai-Tai. EXISTENCE OF GLOBAL ATTRACTORS FOR A NONLINEAR EVOLUTION EQUATION IN SOBOLEV SPACE H^k [J]. Acta mathematica scientia,Series B, 2009, 29(5): 1165-1172.
[7]	YANG Ling-E, GUO Bai-Ling. GLOBAL ATTRACTOR FOR CAMASSA-HOLM TYPE EQUATIONS WITH DISSIPATIVE TERM [J]. Acta mathematica scientia,Series B, 2005, 25(4): 621-628.
[8]	CHEN Zhong-Hua, ZHANG Chu-Jing, CHEN Lan-Sun. ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE 1 [J]. Acta mathematica scientia,Series B, 2003, 23(4): 440-.
[9]	HAO Bai-Lin, LIN Guo-An. A REMARK ON THE ATTRACTORS OF NON-NEWTONIAN FLUIDS [J]. Acta mathematica scientia,Series B, 2003, 23(3): 316-.
[10]	Tian Lixin, Xu Zheuyuau, Lu Diauchen. APPROXIMATE INERTIAL MANIFOLDS UNDER NONSELFADJOINT [J]. Acta mathematica scientia,Series B, 1998, 18(S1): 94-104.
[11]	Dai Zhengde, Guo Boling, Chen Fengxin. GLOBAL ATTRACTOR OF A CLASS OF STRONGLY DAMPED NONLINEAR WAVE EQUATIONS [J]. Acta mathematica scientia,Series B, 1998, 18(4): 404-412.
[12]	Guo Boling, Wang Bixiang. UPPER SEMICONTINUITY OF ATTRACTORS FOR THE REACTION DIFFUSION EQUATION [J]. Acta mathematica scientia,Series B, 1998, 18(2): 139-145.