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Paper IPM / M / 16332  


Abstract:  
his paper deals with the blowâup phenomenon to the following quasiâlinear pseudoâparabolic equation with nonlocal source:
u t â Î u t â â Â· (  â u  2 q â u ) = u p ( x , t ) â« Î© K ( x , y ) u p + 1 ( y , t ) d y , x , y â Î© , t > 0 ,
where Î© â â n , n â¥ 3 , is a bounded domain with smooth boundary. Here, 0â<âqââ¤âp and K(x,y) is an integrable realâvalued function. We show that for qâ<âp, the blowâup occurs in finite time with suitable initial data and arbitrary positive initial energy. We also state some key results based on the conception of limiting the energy function in the case of nonnegative initial energy. Besides, we obtain the exact blowâup time under some certain conditions.
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