SLOWLY VARYING JUMP AND TRANSITION PHENOMENA ASSOCIATED WITH ALGEBRAIC BIFURCATION PROBLEMS

被引:122
作者
HABERMAN, R [1 ]
机构
[1] OHIO STATE UNIV,DEPT MATH,COLUMBUS,OH 43210
关键词
D O I
10.1137/0137006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Parameter-dependent equilibrium solutions are analyzed as the parameter slowly varies through critical values corresponding to a bifurcation or to a jump phenomena. At these critical times, interior nonlinear transition layers are necessary. Depending on the particular situation, local scaling analysis yields the first and a second Painleve transcendent among other generic equations. In specific cases the resulting boundary layer solutions either increase algebraically or explode (via a singularity). The algebraic growth corresponds to a smooth transition to a bifurcated equilibrium. When a jump phenomena is expected, an explosion can occur. In this case, the solution of first-order differential equations approaches the equilibrium, describing the slow evolution through such a jump. However, second-order differential equations have finite amplitude oscillations around the new equilibrium.
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页码:69 / 106
页数:38
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