Acta mathematica scientia, Series B >
ON THE EMDEN-FOWLER EQUATION u"(t)u(t)=c1+c2u' (t)2 WITH c1≥0, c2 ≥0
Received date: 2007-12-20
Online published: 2010-07-20
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There are more discussion which concern nonlinear differential equation in [13]
In this article, we study the following initial value problem for the nonlinear equation
{ u"u( t) =c1+c2u' (t)2, c1≥ 0, c2 ≥ 0,
u(0)=u0, u' (0)=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions.
Key words： Blow-up; Life-span; Blow-up constant; asymptotic behavior; null
LI Ming-Rong . ON THE EMDEN-FOWLER EQUATION u"(t)u(t)=c1+c2u' (t)2 WITH c1≥0, c2 ≥0[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1227 -1234 . DOI: 10.1016/S0252-9602(10)60119-1
[1] Li Mengrong. On the Differential Equation u"-lu|p-1u=0. Nonlinear Analysis, 2006, 64: 1025--1056
[2] Li Mengrong. On the blow-up time and blow-up rate of positive solutions of semi-linear wave equations ?u-up=0 in 1-dimensional space. CPAA, 2009 to appear
[3] Li Mengrong. Estimates for the life-span of solutions of semilinear wave equations. CPAA, 2008, 7(2): 417--432
[4] Li Mengrong, Pai Jente. Quenching problem in some semilinear wave equations. Acta Mathematica Scientia, 2008, 28(3): 523--529
[5] Li Mengrong. Existence and uniqueness of solutions of quasilinear wave equations (II). Bulletin Ins Math Academia Sinica, 2006, 1(2): 263--279
[6] Li Mengrong. On The Semilinear Wave Equations. Taiwanese Journal of Mathematics, 1998, 2(3): 329--345
[7] Li Mengrong. Estimates for the life-span of solutions for semilinear wave equations//Proceedings of the Workshop on Differential Equations V. Taiwan: National Tsing -Hua Uni Hsinchu, 1997: 129--138
[8] Li Mengrong, Tsai Longyi. On a system of nonlinear wave equations. Taiwanese Journal of Mathematics. 2003, 7(4): 557--573
[9] Li Mengrong, Tsai Longyi. Existence and nonexistence of global solutions of some systems of semilinear wave equations. Nonlinear Analysis, 2003, 54: 1397--1415
[10] Li Mengrong. Blow-up solutions to the nonlinear second order differential equation. Taiwanese Journal of Mathematics. 2008, 12(3): 599--621
[11] Li Mengrong, Lin Zinghung. Regularity and blow-up constants of solutions for nonlinear differential equation u"-up=0. Taiwanese Journal of Mathematics, 2006, 10(3): 777--796
[12] Chen I-Chen. Some Studies in Differential Equation. National Chengchi University, 1999
[13] Corduneanu C. Principle of Differential and Integral Equations. Boston: Allyn and Bacon, Inc, 1971
[14] Duan Renjun, Li Mengrong, Yang Tong. Propagation of Singularities in the Solutions to the Boltzmann Equation near Equilibrium.
Mathematical Models and Methods in Applied Sciences (M3AS), 2008, 18(7): 1093--1114
[15] Li Mengrong, Chang Yueloong. On a particular Emden-Fowler Equation with non-positive energy-Mathematical model of enterprise
competitiveness and performance. Applied Math Letters, 2007, 20(9): 1011--1015
[16] Shieh T H, Liou T M, Li M R, et al. Analysis on numerical results for stage separation with different exhaust holes. International communications in heat and mass transfer, 2009, 36(4): 342--345
[17] Shieh Tzonghann, Li Mengrong. Numeric treatment of contact discontinuity with multi-gases. Journal of computational and applied mathematics, 2009, 230(2): 656--673
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