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

Guo Ai

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Guo Ai. Initial Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 640-646.

Citation:

Guo Ai. Initial Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 640-646.

Citation:

Guo Ai. Initial Value Problems for a Class of Nonlinear Integro-Partial Differential Equations[J]. Applied Mathematics and Mechanics, 1999, 20(6): 640-646.

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

Guo Ai

Gansu University of Technology, Lanzhou 730050, P R China

Received Date: 1997-08-11
Rev Recd Date: 1998-03-15
Publish Date: 1999-06-15

Abstract

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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References(4)

References

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[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.