一类可扩充杆横截挠度方程的Cauchy问题

The Cauchy Problems of a class of Equations for the Tension of Extensible Beam

讨论一类刻划可扩充杆横截挠度的非线性双曲型方程 utt+A2 u+M(x,‖ A1 / 2 u‖ 22 ) Au=0 ,这里 A=-Δ+I,x∈ Rn,Cauchy问题解的存在唯一性 ,给出了此方程有唯一局部解的存在定理 .文章所给出的结果的适用性要远大于已有的与此问题相关的结论 ,对此方程非线性项的假设要比一般的多 .事实上 。

This paper deals with the hyperbolic equation in the form of u tt +A 2u+M(x,‖A 1/2 u‖ 2 2)Au=0, \$\$which comes from the mathematical description of the tension of a extensible beam, and the existence and uniqueness of Cauchy problems for this equation are presented here. An existence and uniqueness theorem of local solvability is proven for this equation, and compared with the existing results, the author's conditions restricted to the nonlinear term of this equation are much general. In fact, the results given here are obtained by breaking all the former restrictions on the nonlinear term.