一类带有奇异项和对数非局部源的抛物方程解的性质

Study on the solution of a singular nonlocal parabolic equation with logarithmic nonlinearity

研究了具有奇异项和对数非局部源的抛物方程的齐次Neumann初边值问题.利用截断函数思想给出了弱解的局部存在唯一性,并利用修正位势井及对数Sobolev不等式和Hardy-Sobolev不等式给出了弱解的整体存在性及衰退估计,在适当的条件下得到了解在无穷远处爆破.

It was studied a nonlocal parabolic equation with logarithmic nonlinearity in a bounded domain,subject to homogeneous Neumann boundary value condition.Firstly,the idea of truncation functions was used to obtain the local existence and uniqueness of weak solutions.Secondly,modified potential wells,logarithmic Sobolev inequality and Hardy-Sobolev inequality were used to obtain the global existence and decay of the weak solutions.Finally,the results of the blow up in the infinity time also has been given.