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1、?26?2?J?Vol. 26 No. 2 2003?4?ACTA MATHEMATICAE APPLICATAE SINICAApr., 2003eSI?bHAUXF?DK?Qmon(Z?K?i?Z?313000)id?Yk?S?nx?cW?a?q?a?q?sYk?Oh?JPB?nx?a?1fc?Aoy?t?(b?)dX?b?Y?Fx?Qh?ABP?dX?13.?HdX?47?t?y?v?RT?dX?I?yp?oAoy?dXy?+ yy? yn= 0,x (0,1), n Z,(1)y(0) = ,(2)y(1) = ,(3)?0 0,C?lim yi0= .?Byi0?ry0?(9)?yi
2、0= ktanh?12k( + c2)? ,(yi0)2 k2,(10)Wyi0= kcoth?12k( + c2)? ,(yi0)2 k2,(11)?c2?L?M?WM?TL?P?(10), (11)?Lk?fk 0.j?kWc2,C?rW?rp?e?zn ?= 2Wn = 2?T?e?b?wwT?t?W?2n ?= 2ZCVa1)NYL?jhWO0,1ElG?Mxb= 0?(7),?B? = x/.dX(1)(3)?r?F?(6)?yor.mQ?p?r?xOyi0?m?ry0r?E?s?r?cm?(y0r)i=? (2n 2 + n)1/(2n),n?L,(2n 2 + n)1/(2n),
3、n?L?n ?= 2.2?Sq?nx?cW?a?q361?m?r?xO(10), (11)?x?E?s?xO?r?cm?(yi0)0= k 0.J?e?k =? (2n 2 + n)1/(2n),n?L,(2n 2 + n)1/(2n),n?L?n ?= 2.?k 0,N?k = (2n 2 + n)1/(2n),n ?= 2 (?B?L?LX?D),(12)?2n 2 + n 0,?n?L(n ?= 2)B? 0.?(10)(12)e?yi0= ktanh?k2( + c2)? ,(yi0)2 k2(13)Wyi0= kcoth?k2( + c2)? ,yi0 k,(14)?k = (2n
4、2 + n)1/(2n).?tZl(2),?(13), (14)? = 0 (Q?x = 0?)?C?yi0(0) = ,N? = (2n 2 + n)1/(2n)tanh?12(2n 2 + n)1/(2n)c2? ,(15)? = (2n 2 + n)1/(2n)coth?12(2n 2 + n)1/(2n)c2? .(16)?(15)?(16)f?c2.?(12)?2n 2 n,?n?LB 0,?(15), (16)eM?WM?TL?y? (2n 2 + n)1/(2n)B?r?xOyi0?(14)?(2n 2 + n)1/(2n) 2 n, (2n 2 + n)1/(2n)B(n?LB
5、?Zl 0),dX(1)(3)?b?r?y(x) =?(2 n)x + 2n 2 + n?1/(2n)+ k? coth?k2?x+ c2? 1? + O(),(17)?k = (2n 2 + n)1/(2n), 0 2n, (2n2+n)1/(2n) 0,P?n?LB?k = (2n+ 2 n)1/(2n) 0,2n+ 2 n 0,2n+ 2 n 0, 0.(20)?(10), (11)W(19), (20)? (a)?n?LB?yi0= (2n+ 2 n)1/(2n)tanh? 1 2(2n+ 2 n)1/(2n)( + c2)? ,(yi0)2 (2n+ 2 n)2/(2n),(21)y
6、i0= (2n+ 2 n)1/(2n)coth? 1 2(2n+ 2 n)1/(2n)( + c2)? ,yi0 (2n+ 2 n)1/(2n).(22)?tZl(3),?(21), (22)? = 0 (Q?x = 1?)?C?yi0(0) = ,N? = (2n+ 2 n)1/(2n)tanh? 1 2(2n+ 2 n)c2? ,(23) = (2n+ 2 n)2ncoth? 1 2(2n+ 2 n)c2? .(24)?(23)?(24)f?c2.?(19)?2n+ 2 n 0, 0,?(27), (28)eM?WM?TL?y?2n+ 2 n 0, 0, 0, 0, | 0, 0, 0,
7、0, | 0, 0.(34)?(y0r)i=? ?(2 n)xb+ 2n 2 + n?1/(2n),n?L,?(2 n)xb+ 2n 2 + n?1/(2n),n?L?n ?= 2.?(yi0)0= k.J?e?k =?(2 n)x b+ 2n 2 + n?1/(2n).(35)?B(2 n)xb+ 2n 2 + n 0,?n?L(n ?= 2)B? 0.?F?e?(34), (35)? (a)?n?LB?k =?(2n)x b+2n?1/(2n), k =?(2n)x b+2n2+n?1/(2n).?xb=1 2(2 n)(2n 2n) +1 2,k =?12(2n 2n) 2 n 2?1/
8、(2n) .(36)(b)?n?L?n ?= 2B?k = ?(2 n)xb+ 2n?1/(2n),k =?(2 n)x b+ 2n 2 + n?1/(2n).?H?D?xbWk,?z?n?L(n ?= 2)B?b?i0,1?l?n?LB?xO?r?F(10)?vD?fyi0= k tanh?k2? ,(37)?k =?12(2n2n)(2n)/2?1/(2n),?b?d?x = xb(f = 0),P? c2= 0.2?Sq?nx?cW?a?q365?0 0,P?(36)?1 2 n.?dXX?r?M?p? (VII)?n?L?1 2 nB?dX(1)(3)?b?r?y(x) = ?(2 n
9、)x + 2n?1/(2n)+ k? tanhk(x xb) 2+ 1? + O(),0 x 2 n, (2n 2 + n)1/(2n)B(n?LB? 0),dX (1)(3)?v?(17)?b?r?r?x = 0Fx? (II)?2n 2 n, | 0, 0, 0, 0, | 2 nB?dX(1)(3)?v?(38)?b?r?r?x = xb (0,1)Fx? (VIII)?n?LB?dX(1)(3)? (IX)?Q?v?dX(1)(3)fb?r? (X)?(I)?(VII)?Q?KL?B?N?H?H?b?r?3n = 2ZCVa?O?H?jp?(n = 2): (I)? 0, e1B?dX
10、(1)(3)?v?y(x) = ex1+ e1? cothe1 2?x+ c2? 1? + O(),0 0, | e1B?dX(1)(3)?v?y(x) = ex1+ e1? tanhe1 2?x+ c2? 1? + O(),0 ? 1366?I?26?b?r?Q?tx = 0Fx? (III)? 0, | eB?dX(1)(3)?v?y(x) = ex e? tanhe 2?x 1+ c2? 1? + O(),0 ? 1?b?r?Q?tx = 1Fx? (IV)? 0, eB?dX(1)(3)?v?y(x) = ex e? cothe 2?x 1+ c2? 1? + O(),0 ? 1?b?
11、r?Q?tx = 1Fx? (V)?Q?v?dX(1)(3)fb?r? (VI)dX(1)(3)f?b?r? (VII)?Hg?v?f?B?f?H?H?b?r?HBgR?e?n?LB?b?r?k?bV?tzG?j?U?u?R?1 OMalley, Jr, R E. On the Asymptotic Solution of the Singularly Perturbed Boundary Value Problems Posed by Boh e.J. Math. Anal. Appl., 2000, 242: 18382 Laforgue J G, OMalley, Jr, R E.Sho
12、ck Layer Movement for Burgers Equation.SIAM J. Appl.Math., 1995, 55: 332348 3 Nayfeh A H. Introduction to Perturbed Techniques.New York: John Weiley&Sons, 1981, 3653754 Mo Jiaqi, Ouyang Cheng. A Class of Nonlocal Boundary Value Problems of Nonlinear Elliptic Systemsin Unbounded Domains.Acta Math. Sc
13、i. (Series B), 2001, 21(1): 9397 5 Mo Jiaqi, Ouyang Cheng. A Class of Singularly Perturbed Generalized Boundary Value Problems forQuasi-linear Elliptic Equations of Higher Order.Appl. Math. Mech., 2001, 22(3): 3723786 Boh e A.The Shock Location for a Class of Sensitive Boundary Value Problems.J. Math. Anal.Appl., 1999, 235: 295314 7 Mo Jiaqi.A Class of Singularly Perturbed Reaction D
