一类非线性积分偏微分方程的初值问题

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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

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[4]	MacCamy R C.A model for one dimensional nonlinear viscoelasticity[J].Quart Appl Math,1977,35:21~33.

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