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Using the boundary layer corrective method, one type of perturbed model with delays in classical physics is studied. The asymptotic solution for the model is constructed. The asymptotic behaviors of the solution are also discussed.
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Keywords:
- classical physics /
- perturbation /
- approximate solution
[1] Feng G L, Dong W J, Jia X J 2002 Acta Phys.Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[2] Feng G L, Dia X G, Wang A H 2001 Acta Phys.Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧等 2001 50 606]
[3] Lin W T, Ji Z Z, Wang B 2002 Prog. Natur. Sci. 12 102 (in Chinese) [林万涛、季仲贞、王斌 2002 自然科学进展 12 102]
[4] Wang L S, Xu D Y 2003 Sci. China E 32 488 (in Chinese) [王林山、徐道义 2003 中国科学 E 32 488]
[5] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1689 (in Chinese) [莫嘉琪、林万涛 2008 57 1689]
[6] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Chin. Phys. B 18 3661
[7] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1291 (in Chinese) [莫嘉琪、林万涛 2008 57 1291]
[8] Jordan G S 1978 Proc. Roy. Soc. Edinburgh Sect. A 80 235
[9] Ni M K, Lin W Z 2009 Asymptotic for Singular Perturbed Problem( Beijing:Higher Education Press) p35 (in Chinese) [倪明康、林武忠 2009 奇异摄动问题中的渐近理论 (北京:高等教育出版社) 第35页]
[10] Il’in A M 1991 Matching of asymptotic expansions of solutions of boundary value problem (American Mathematical Society Providence, Rhode Island) p27
[11] Mo J Q, Lin W T 2005 Appl. Math. J. Chinese Univ. Ser. B 20 159
[12] Mo J Q, Liu S D, Tang R R 2010 Acta Phys.Sin. 59 4403 (in Chinese) [莫嘉琪、刘树德、 唐荣荣 2010 59 4403]
[13] Jiao X Y, Lou Y S 2009 Chin. Phys. B 18 3611
[14] Mo J Q 2009 Chin. Phys.Lett. 26 060202
[15] Mo J Q 2009 Chin. Phys.Lett. 26 010204
[16] Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、 何铭 2007 56 1843]
[17] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys.Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、 陈贤峰 2007 56 6169]
[18] Mo J Q, Cheng Y 2009 Acta Phys.Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 58 4379]
[19] Li B Q, Ma Y L 2009 Acta Phys.Sin. 58 4373 (in Chinese) [李帮庆、马玉兰 2009 58 4373]
[20] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5887 (in Chinese) [套格图桑、斯仁道尔吉2009 58 5887]
[21] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys.Sin. 57 11 (in Chinese) [马松华、吴小红、方建平、郑春龙 2008 57 11]
[22] Mo J Q, Zhang W J, He M 2006 Acta Phys. Sin. 55 3233 (in Chinese) [莫嘉琪、张伟江、 何铭 2007 55 3233]
[23] Mo J Q 2009 Sci. Chin. Ser. G 52 1007
[24] Lin W T, Mo J Q, Zhang W J, Chen X F 2008 Acta Phys.Sin. 57 4641 (in Chinese) [林万涛、莫嘉琪、张伟江、陈贤峰 2008 57 4641]
[25] Mo J Q, Lin W T 2008 J. Sys.Sci.&. Complexity 20 119
[26] Chen H J, Mo J Q 2010 Acta Phys.Sin. 59 4409 (in Chinese) [陈怀军、 莫嘉琪 2010 59 4409]
[27] Mo J Q, Lin W T 2008 Acta Math. Appl. Sin. 22 277
[28] Mo J Q, Tang R R 2007 Acta Math. Sin. 27 296
[29] Nicaise S, Pignotti C 2006 SIAM Journal on Control and Optimization 45 1561
[30] Vasil’eva A B, Butuzov V F 2008 Asymptotic Methods in Singular-Perturbation Theory Translated by Ni M K and Lin W Z (Beijing:Higher Education Press) p44 (in Chinese)
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[1] Feng G L, Dong W J, Jia X J 2002 Acta Phys.Sin. 51 1181 (in Chinese) [封国林、董文杰、贾晓静 2002 51 1181]
[2] Feng G L, Dia X G, Wang A H 2001 Acta Phys.Sin. 50 606 (in Chinese) [封国林、戴新刚、王爱慧等 2001 50 606]
[3] Lin W T, Ji Z Z, Wang B 2002 Prog. Natur. Sci. 12 102 (in Chinese) [林万涛、季仲贞、王斌 2002 自然科学进展 12 102]
[4] Wang L S, Xu D Y 2003 Sci. China E 32 488 (in Chinese) [王林山、徐道义 2003 中国科学 E 32 488]
[5] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1689 (in Chinese) [莫嘉琪、林万涛 2008 57 1689]
[6] Zhou X C, Lin Y H, Lin W T, Mo J Q 2009 Chin. Phys. B 18 3661
[7] Mo J Q, Lin W T 2008 Acta Phys.Sin. 57 1291 (in Chinese) [莫嘉琪、林万涛 2008 57 1291]
[8] Jordan G S 1978 Proc. Roy. Soc. Edinburgh Sect. A 80 235
[9] Ni M K, Lin W Z 2009 Asymptotic for Singular Perturbed Problem( Beijing:Higher Education Press) p35 (in Chinese) [倪明康、林武忠 2009 奇异摄动问题中的渐近理论 (北京:高等教育出版社) 第35页]
[10] Il’in A M 1991 Matching of asymptotic expansions of solutions of boundary value problem (American Mathematical Society Providence, Rhode Island) p27
[11] Mo J Q, Lin W T 2005 Appl. Math. J. Chinese Univ. Ser. B 20 159
[12] Mo J Q, Liu S D, Tang R R 2010 Acta Phys.Sin. 59 4403 (in Chinese) [莫嘉琪、刘树德、 唐荣荣 2010 59 4403]
[13] Jiao X Y, Lou Y S 2009 Chin. Phys. B 18 3611
[14] Mo J Q 2009 Chin. Phys.Lett. 26 060202
[15] Mo J Q 2009 Chin. Phys.Lett. 26 010204
[16] Mo J Q, Zhang W J, He M 2007 Acta Phys. Sin. 56 1843 (in Chinese) [莫嘉琪、张伟江、 何铭 2007 56 1843]
[17] Mo J Q, Zhang W J, Chen X F 2007 Acta Phys.Sin. 56 6169 (in Chinese) [莫嘉琪、张伟江、 陈贤峰 2007 56 6169]
[18] Mo J Q, Cheng Y 2009 Acta Phys.Sin. 58 4379 (in Chinese) [莫嘉琪、程燕 2009 58 4379]
[19] Li B Q, Ma Y L 2009 Acta Phys.Sin. 58 4373 (in Chinese) [李帮庆、马玉兰 2009 58 4373]
[20] Taogetusang, Sirendaoerji 2009 Acta Phys.Sin. 58 5887 (in Chinese) [套格图桑、斯仁道尔吉2009 58 5887]
[21] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta Phys.Sin. 57 11 (in Chinese) [马松华、吴小红、方建平、郑春龙 2008 57 11]
[22] Mo J Q, Zhang W J, He M 2006 Acta Phys. Sin. 55 3233 (in Chinese) [莫嘉琪、张伟江、 何铭 2007 55 3233]
[23] Mo J Q 2009 Sci. Chin. Ser. G 52 1007
[24] Lin W T, Mo J Q, Zhang W J, Chen X F 2008 Acta Phys.Sin. 57 4641 (in Chinese) [林万涛、莫嘉琪、张伟江、陈贤峰 2008 57 4641]
[25] Mo J Q, Lin W T 2008 J. Sys.Sci.&. Complexity 20 119
[26] Chen H J, Mo J Q 2010 Acta Phys.Sin. 59 4409 (in Chinese) [陈怀军、 莫嘉琪 2010 59 4409]
[27] Mo J Q, Lin W T 2008 Acta Math. Appl. Sin. 22 277
[28] Mo J Q, Tang R R 2007 Acta Math. Sin. 27 296
[29] Nicaise S, Pignotti C 2006 SIAM Journal on Control and Optimization 45 1561
[30] Vasil’eva A B, Butuzov V F 2008 Asymptotic Methods in Singular-Perturbation Theory Translated by Ni M K and Lin W Z (Beijing:Higher Education Press) p44 (in Chinese)
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