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The expressions of shock solutions for singularly perturbed Robin problem of nonlinear equations are constructed using the matching method. The conditions for appearance of shock near the boundary are discussed.
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Keywords:
- quasilinear equation /
- shock solution /
- internal layer /
- boundary layer
[1] Wang M L 1995 Phys. Lett. A 199 169
[2] Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、 韩家骅、 史良马、 张 苗 2006 55 3858]
[3] Li X Z, Li X Y, Zhang L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese) [李向正、 李修勇、 赵丽英、 张金良 2006 57 2203]
[4] Li Z B, Zhang S Q 1997 Acta Math. Phys. Sin. 17 81 (in Chinese) [李志斌、 张善卿 1997 数学 17 81]
[5] Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese) [高 亮、 徐 伟、 唐亚宁、 申建伟 2007 56 1860]
[6] 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]
[7] Bekir A 2008 Phys. Lett. A 372 2254
[8] Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese) [李帮庆、 马玉兰 2009 58 4373]
[9] Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、 强继业、 方建平 2007 56 620]
[10] Ma S H, Qiang J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[11] Loutsenko I 2006 Comm. Math. Phys. 268 465
[12] Parkes E J 2008 Chaos Soliton. Fract. 38 154
[13] Graef J R, Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489
[14] Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297
[15] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[16] Ramos M 2009 J. Math. Anal. Appl. 352 246
[17] 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]
[18] 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]
[19] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[20] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[21] Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、 姚静荪 2009 58 7419]
[22] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[23] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[24] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程 燕 2009 58 4379]
[25] Mo J Q 2009 Sci. Chin. Ser. G 52 1007
[26] Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[27] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪、 林万涛、 林一骅 2007 56 3127]
[28] Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6689 (in Chinese) [莫嘉琪、 林万涛 2008 57 6689]
[29] Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 58 6692]
[30] Mo J Q, Lin S R 2009 Chin. Phys. B 18 3628
[31] Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[32] Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
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[1] Wang M L 1995 Phys. Lett. A 199 169
[2] Wu G J, Han J H, Shi L M, Zhang M 2006 Acta Phys. Sin. 55 3858 (in Chinese) [吴国将、 韩家骅、 史良马、 张 苗 2006 55 3858]
[3] Li X Z, Li X Y, Zhang L Y, Zhang J L 2008 Acta Phys. Sin. 57 2203 (in Chinese) [李向正、 李修勇、 赵丽英、 张金良 2006 57 2203]
[4] Li Z B, Zhang S Q 1997 Acta Math. Phys. Sin. 17 81 (in Chinese) [李志斌、 张善卿 1997 数学 17 81]
[5] Gao L, Xu W, Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860 (in Chinese) [高 亮、 徐 伟、 唐亚宁、 申建伟 2007 56 1860]
[6] 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]
[7] Bekir A 2008 Phys. Lett. A 372 2254
[8] Li B Q, Ma Y L 2009 Acta Phys. Sin. 58 4373 (in Chinese) [李帮庆、 马玉兰 2009 58 4373]
[9] Ma S H, Qiang J Y, Fang J P 2007 Acta Phys. Sin. 56 620 (in Chinese) [马松华、 强继业、 方建平 2007 56 620]
[10] Ma S H, Qiang J Y, Fang J P 2007 Comm. Theor. Phys. 48 662
[11] Loutsenko I 2006 Comm. Math. Phys. 268 465
[12] Parkes E J 2008 Chaos Soliton. Fract. 38 154
[13] Graef J R, Kong L 2008 Math. Proc.Camb. Philos. Soc. 145 489
[14] Hovhannisyan G, Vulanovic R 2008 Nonlinear Stud. 15 297
[15] Barbu L, Cosma E 2009 J. Math. Anal. Appl. 351 392
[16] Ramos M 2009 J. Math. Anal. Appl. 352 246
[17] 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]
[18] 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]
[19] Mo J Q 2009 Chin. Phys. Lett. 26 010204
[20] Mo J Q 2009 Acta Phys. Sin. 58 695 (in Chinese) [莫嘉琪 2009 58 695]
[21] Mo J Q, Yao J S 2009 Acta Phys. Sin. 58 7419 (in Chinese) [莫嘉琪、 姚静荪 2009 58 7419]
[22] Mo J Q 2009 Chin. Phys. Lett. 26 060202
[23] Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese) [莫嘉琪 2009 58 2930]
[24] Mo J Q, Cheng Y 2009 Acta Phys. Sin. 58 4379 (in Chinese) [莫嘉琪、程 燕 2009 58 4379]
[25] Mo J Q 2009 Sci. Chin. Ser. G 52 1007
[26] Mo J Q, Lin W T, Wang H 2008 Chin. Geographical Sci. 18 193
[27] Mo J Q, Lin W T, Lin Y H 2007 Acta Phys. Sin. 56 3127 (in Chinese) [莫嘉琪、 林万涛、 林一骅 2007 56 3127]
[28] Mo J Q, Lin W T 2008 Acta Phys. Sin. 57 6689 (in Chinese) [莫嘉琪、 林万涛 2008 57 6689]
[29] Mo J Q, Lin Y H, Lin W T 2009 Acta Phys. Sin. 58 6692 (in Chinese) [莫嘉琪、 林一骅、 林万涛 2009 58 6692]
[30] Mo J Q, Lin S R 2009 Chin. Phys. B 18 3628
[31] Mo J Q, Lin W T 2008 Chin. Phys. B 17 370
[32] Mo J Q, Lin W T 2008 Chin. Phys. B 17 743
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