一类伪抛物型方程非局部问题解的爆破性
The blow up property of solutions for a pseudoparabolic equation with nonlinear nonlocal source

研究带非线性非局部源项的伪抛物方程的一类初边值问题，考虑非局源项是在时间上的积分. 首先利用严格压缩映射和不动点理论证明解的局部存在性； 然后通过特征函数法结合微分不等式组新性质的一个变体法证明其解在一定条件下的爆破性质； 最后给出该模型的特殊情况，并证明了相应问题解的爆破性和全局存在性.
We investigate some initial boundary value problem of pseudoparabolic equations with nonlinear nonlocal sources.We consider the integral of the nonlocal in time.First，by the use of constructing mapping and the fixed point theory，we prove the existence of local solutions.Secondly，we obtain that the solutions blow up relys on a variant of the eigenfunction method combined with new properties on systems of differential inequations.Finally，we derive the corresponding solutions blow up and global existence of the special case of the model