Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations

Cui Shang-bin; Qu Chang-zheng

Volume 15 Issue 4

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1994 > 15(4): 365-379

Cui Shang-bin, Qu Chang-zheng. Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1994, 15(4): 365-379.

Citation:

Cui Shang-bin, Qu Chang-zheng. Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1994, 15(4): 365-379.

Citation:

Cui Shang-bin, Qu Chang-zheng. Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1994, 15(4): 365-379.

PDF( 2826 KB)

Initlal Boundary Value Problems for a Class of Nonlinear Integro-Partial Differential Equations

Cui Shang-bin¹,
Qu Chang-zheng²

1.
Dept. of Math. , Lanzhou Univ. , Lanzhou;
2.
Dept. of Math. , Northwest Univ. , Xi'an

Received Date: 1992-11-06
Publish Date: 1994-04-15

Abstract

Abstract

This paper studies the global existence of the classical solutions to the following problem: This problem describes the nonlinear vibrations of finite rods with nonlinear vis-coelasticity.Under certain conditions on σ and f,we obtained the unique existence of the global classical solution of this problem.
- integro-partial differential equation,
- initial value problem,
- global classical solution

FullText(HTML)

References(15)

References

[1]	Christensen,R.M.,Theory of Viscoelasticity,An Introduction,2nd edition,Academic Press,New York(1982).
[2]	Renardy,M.,W.E.Hrusa and J.A.Nohel.Mathematical problems in Viscoelastity,Longman Group,Boston-London-Melbourne(1987).
[3]	MacCamy,R.C.,A modol for one-dimcnsional nonlinoar viscc-lasticity,Qyart.Appl.Math.,35(1977),21-33.
[4]	Dafermos,C.M.and J.A.Nohel,Energy methods for nonlinear hyperbolic Volterra integrodifferontial(quatioos,Comm.Partial Differential Equations,4(1979),219-278.
[5]	Dafermos,C.M.and J.A.Nohel,A nonlinear hyPperbolic Volterra equation in viscoelasticity,Amer.Math.J.,Supplement(1981),87-116.
[6]	Hrusa.W.and M.Renardy.On wave propagation in linoar visce-elasticity,Quart.Appl.Math.,43(1985),237-253.
[7]	Hrusa,W.and J.A.Nohel,The Cauchy problem in one-dimensional nonlinear viscoelasticity,J.Diff.Equa.,59(1985),388-412.
[8]	Engler,H.,Weak solutions of a class of quosilinear hyperbolic integro-differential equations describing viscoelastic materials,Arch.Rafional Mech.Anal.,113(1991),1-38.
[9]	崔尚斌,半线性卷积双曲型积分微分方程的初边值问题,应用数学学报,11(3)(1988),271-286.
[10]	屈长征,关于两类方程的解,兰州大学学报,25(4)(1989),5-14.
[11]	崔尚斌、马玉兰,一类半线性积分微分方程初边值问题的整体解和爆破解.应用数学,6(4)(1993),445-451.
[12]	Dafermos,C.A.,Developmont of singularities in the motion of materials with fading memory,Arch.Rational Mech.Anal.,91(1956),193-205.
[13]	Klainerman,S.and A.Majda,Formation of singularities for wave equations including the nonlinear vibrating string.Comm.Pure Appl.Math.,33(1980),241-263.
[14]	陈予恕,《非线性振动》,天津科学技水出版社(1983).
[15]	张恭庆,《临界点理论及其应用》,上海科学技术出版社(1986).

Relative Articles

[1]	YIN Zihan, KANG Jing. Dispersive Quantization of 2D Linear Dispersive Equations[J]. Applied Mathematics and Mechanics, 2021, 42(7): 741-750. doi: 10.21656/1000-0887.410142
[2]	FANG Shao-mei, JIN Ling-yu, GUO Bo-ling. Global Existence of Solutions of the Periodic Initial Value Problems for Two-Dimensional Newton-Boussinesq Equations[J]. Applied Mathematics and Mechanics, 2010, 31(4): 379-388. doi: 10.3879/j.issn.1000-0887.2010.04.001
[3]	FANG Shao-mei, GUO Bo-ling. Initial-Boundary Value Problem of One Class Nonlinear Schrêdinger Equations Described in Molecular Crystals[J]. Applied Mathematics and Mechanics, 2008, 29(2): 127-132.
[4]	WANG Yan-ping, GUO Bo-ling. Blow-up of the Solution for a Generalized Boussinesq Equation[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1281-1286.
[5]	SHEN Chun, WANG Yue-peng, SHI Wei. Stability of System of Two-Dimensional Non-Hydrostatic Revolving Fluids[J]. Applied Mathematics and Mechanics, 2006, 27(3): 285-292.
[6]	SONG Chang-ming. Nonexistence of Global Solutions of a Nonlinear Hyperbolic Equation With Material Damping[J]. Applied Mathematics and Mechanics, 2006, 27(7): 852-858.
[7]	WANG Yue-peng. Well Posedness of Initial Value Problem for Euler Equations of Inviscid Compressible Adiabatic Fluid[J]. Applied Mathematics and Mechanics, 2005, 26(7): 794-800.
[8]	SHANG Ya-dong, GUO Bo-ling. Analysis of Chebyshev Pseudospectral Method for Multi-Dimensional Generalized SRLW Equations[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1035-1048.
[9]	JIANG Fu-ru. On the Asymptotic Solutions of Boundary Value Problems for a Class of Systems of Nonlinear Differential Equations(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(3): 239-249.
[10]	JIANG Fu-ru, JIN Qi-nian. Asymptotic Solutions of Boundary Value Problems for Third Order Ordinary Differential Equations With Turning Points[J]. Applied Mathematics and Mechanics, 2001, 22(4): 345-353.
[11]	XIONG Yue-shan, Onyx Wai Wing hong. The Analytical Solution for Sediment Reaction and Diffusion Equation With Generalized Initial-Boundary Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(4): 354-358.
[12]	Zhang Fubao. Periodic Boundary Value Problems for First Order Integrodifferential Equations of Mixed Type[J]. Applied Mathematics and Mechanics, 2000, 21(3): 323-330.
[13]	Hong Shihuang, Hu Shigeng. Existence of Solutions for Periodic Boundary Value Problem for Second Order Integro-Differential Equations[J]. Applied Mathematics and Mechanics, 2000, 21(3): 315-322.
[14]	Wang Fanbin. Blow-Up and Die-out of Solutions of Nonlinear PseudoHyperbolic Equations of Generalized Nerve Conduction Type[J]. Applied Mathematics and Mechanics, 1996, 17(11): 1039-1043.
[15]	Cai Chongxi, Lin Changhao. Phragmén-Lindelöf Alternative Results for the Initial Boundary Problem of Stokes Equation[J]. Applied Mathematics and Mechanics, 1996, 17(8): 689-698.
[16]	Zhang Xiang. Singular Perturbation of lnitial-boundary Value Problems of Reaction Diffusion Equation with Delay[J]. Applied Mathematics and Mechanics, 1994, 15(3): 253-258.
[17]	Li Wen-shen. The Uniqueness and Existence of Solution of the Charac-teristic Problem on the Generalized KdV Equation[J]. Applied Mathematics and Mechanics, 1994, 15(5): 463-469.
[18]	Yang Dan-ping. A Coupling Method of Difference with High Order Accuracy and Boundary Integral Equation for Evolutionary Equation and Its Error Estimates[J]. Applied Mathematics and Mechanics, 1991, 12(9): 831-844.
[19]	Su Yu-chcng, Lin Ping. An Exponentially Fitted Difference Scheme for the Hyperbolic-hyperbolic Singularly Perturbed Initial-Boundary Value Problem[J]. Applied Mathematics and Mechanics, 1991, 12(3): 219-227.
[20]	Liang Zhong-chao, Chen Shao-zhu. Proper Solutions and Limit Boundary Value Problems of Nonlinear Second-Order Systems of Differential Equations[J]. Applied Mathematics and Mechanics, 1985, 6(11): 1027-1034.