一类非线性积分偏微分方程的初值问题

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

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

摘要: 讨论初值问题整体经典解的存在性。该问题来源于粘弹性力学。在关于已知函数的一些正则性假设和p'(s)≥c₁>0,|q'(s)|≤const,λ(0)<0,λ'(0)<λ²(0)的条件下,通过能量估计,证明了该问题整体经典解的存在性。
- 初值问题 /
- 积分偏微分方程 /
- 经典解
Abstract: In this paper,the problem of global existence of solutions to the followin g initial value problem is studied: which comes from viscoelastic mechanics.By making u se of integral estimates method,it is proved that this problem has a global solution if,in addition to certain regularity assumptions on the given fun ctions,the following conditions are satisfied: p'(s)≥c₁>0,|q'(s)|≤const,λ(0)<0,λ'(0)<λ²(0).
- initial value problem /
- integro-partial differential equation /
- classical solution

[1]	Cui Shangbin.Global solutions for a class of nonlinear integro-differential equations[J].Acta Appl Math Sinica,1993,16(2):191~200.(in Chinese)
[2]	Wang Shubin.Initial boundary value problems and initial value problems of sem ilinearquasi-hyperbo lic integro-differential equation[J].Acta Appl Math Sinica,1995,18(4):567~578.(in Chinese)
[3]	Greenberg J M,MacCam y R C,Mizel V J.On the existence,uniqueness and stability ofso lutions of the equation R(u_x)u_xx+u_xxt=u_tt[J].J Math Mech,1968,17:707~728.
[4]	MacCamy R C.A model for one dimensional nonlinear viscoelasticity[J].Quart Appl Math,1977,35:21~33.