半线性高阶抛物型方程组具慢衰减初值问题整体解的存在与不存在性 Existence and Nonexistence of Global Solutions of Higher-Order Parobolic System with Slow Decay Initial Data

摘要

本文研究一类半线性高阶抛物型方程组的Cauchy问题。通过建立高阶抛物型方程组的所谓“比较原理”，利用Schauder不动点理论和试验函数等方法，证明了该问题在慢衰减初值条件下解的整体性存在性与不存在性。 This paper concerns with the Cauchy problem of a higher-order parobolic system. By constructing a so called “comparison principle”of the higher-order parobolic system and utilizing Schauder fixed point theorem and the test function method, we prove the existence and nonexistence of global solutions to such a problem with slow decay initial data.