一类非线性积分微分方程的初边值问题

崔尚斌; 屈长征

一类非线性积分微分方程的初边值问题

崔尚斌¹,
屈长征²

1.
兰州大学数学系;
2.
西北大学数学系西安

计量
- 文章访问数: 2055
- HTML全文浏览量: 112
- PDF下载量: 493
- 被引次数: 0
出版历程
- 收稿日期: 1992-11-06
- 刊出日期: 1994-04-15

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

摘要

摘要: 本文讨论下列初边值问题整体经典解的存在性：该问题所描述的是一类具有非线性粘弹性的粘弹性杆的非线性振动,在一定条件下,我们证明了该问题整体经典解的存在唯一性.
- 积分微分方程 /
- 初边值问题 /
- 整体经典解
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

HTML全文

参考文献(15)

[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).