Abstract
It's often ignored that in nonlinear partial differential equations, there has the unique solutions in the process of seeking numerical solutions for the system solutions. So the rationality of simplifying an finite-dimensional system cannot be ensured, or even worse, the incorrect conclusions may be resulted in. In this paper, the Sobolev space is used as a tool to improve the existence and uniqueness for the weak solution of a class of nonlinear elastic beam equations, for FPU problem by the way of Galerkin's method and local extension method.
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