一类具有对数非线性项的伪抛物方程解的爆破

Blow-up of solutions for a class of pseudo-parabolic equations with logarithmic nonlinearity

研究了一类具有p-Laplacian算子和对数非线性项的抛物方程的初边值问题.利用凸引理、微分不等式技巧及位势井理论,研究了负初始能量及次临界初始能量下弱解在有限时间爆破,此外,给出了适当假设条件下爆破时间的上界和下界估计.

It was studied that the initial boundary value problem of parabolic equation with p-Laplacian operator and logarithmic nonlinearity.By using convex lemma,differential inequality technique and potential well theory,the blow-up of weak solutions in finite time with negative initial energy and subcritical initial energy was studied.In addition,the upper and lower bounds of blow-up time estimates under appropriate assumptions were given.