【摘要】 研究了两类强阻尼非线性波动方程 utt-αΔut-βΔu =f ( u) 及 utt-αΔut-βΔu =f ( ut) (α>0 ,β≥0 )的初边值问题解的 blow up问题 ;证明了在非线性函数 f ( s)和初始数据的一定假设下 ,这两个方程的初边值问题的解在有限时间内 blow up。更多还原

【Abstract】 In this paper,we study the blow up problems of solutions for the initinl boundary value problems of two classes of strongly damped nonlinear wave equations utt-αΔut-βΔu =f ( u) (α >0 ,β≥ 0 ) , utt-αΔut-βΔu =f ( ut) (α >0 ,β≥ 0 ) It is proved that under certain assumptions on the nonlinear function and the initial data the solutions of the initial boundary value problems of these two equations blow up in finite time.更多还原