伪抛物型方程非局部问题解的爆破性 The Blow up Property of Solutions for Some Pseudoprabolic Equations with Nonlinear Nonlocal Source

摘要

本文研究带非线性非局部源项的伪抛物型方程的一类初边值问题。首先证明了模型局部解的存在唯一性，然后证明其解在一定条件下的爆破性质，最后给出两个特殊源项问题解的爆破速率估计。This paper investigates some Initial Buandary Value Problem (IBVP) of pseudoparabolic equations with nonlinear nonlocal source. Firstly, the authors prove the existence and uniqueness of local solutions of the IBVP. Secondly, authors derive the blow up property of solutions under certain conditions. Finally, they show the growth rate of solutions near the blow up time.