具有非线性边界耗散的四阶方程整体解的不存在性分析

An Analysis of Non Existence of Global Solutions for Four Order Equations with Nonlinear Boundary Dissipation

物理学新现象的出现,在该领域内产生了对孤立子及混沌问题的探究,并出现了一些带有非线性耗散的方程,因此文中将具有非线性边界耗散的四阶方程作为研究对象,并对该方程的整体解进行不存在性分析。首先,运用变分法获取整体弱解的存在性,将Gronwall不等式与Galerkin方法和积分估计法结合进行恰当的先验预估计并研究解的渐近特性,通过积分不等式利用Sobolev嵌入定理和吸引子存在定理证明在内积空间中整体吸引子的存在性,同时得到了吸引子的存在条件;其次,引进位势井和井外集合,运用H?lder不等式与Galerkin方法结合给定初始能量条件,得到整体解存在的门槛结果,在该方程及给定的初始条件满足区间内单调递增条件时,利用反证法可证明方程解不存在整体解,即局部解可在限定时间内实现爆破。

Emergence of new physics,in the field of inquiry has soliton and chaos,and there are some withnonlinear dissipative equations,so the nonlinear boundary dissipation equation of order four as theresearch object,and the overall solution of the equation of non existence analysis.First of all,by usingthe variational method to obtain the existence of global weak solutions,Gronwall inequality and Galerkinintegral estimation method and proper asymptotic behavior of solutions and a priori estimate method,byusing the Sobolev integral inequality theorem and existence theorem to prove the existence of attractorsin the inner space of the global attractor,and the existence condition of attractor the obtained;secondly,introducing a family of potential wells and well set,using H?lder inequality and Galerkin methodcombined with the given initial energy conditions,get the threshold of global existence results in theinitial conditions and the equation satisfies the given interval increasing,using apagoge can prove thatthere is no overall solution the solution,namely the local solution can be achieved within the time limit ofblasting.