Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   By constructing different auxiliary functions and using Hopf’s maximum principle, the sufficient conditions for the blow-up and global solutions are presented for nonlinear parabolic equation  u   t   = ∇( a ( u ) b ( x ) c ( t )∇ u ) +  f ( x ,  u ,  q ,  t ) with different kinds of boundary conditions. The upper bounds of the “blow-up time” and the “upper estimates” of global solutions are provided. Finally, some examples are presented as the application of the obtained results.
['Tong Zhang', 'Yinnian He']
I am writing a research paper on a idea Blow-up and global solutions for a class of nonlinear parabolic equations with different kinds of boundary conditions
[{"from": "human", "value": "I am writing a research paper on a idea Blow-up and global solutions for a class of nonlinear parabolic equations with different kinds of boundary conditions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   By constructing different auxiliary functions and using Hopf\u2019s maximum principle, the sufficient conditions for the blow-up and global solutions are presented for nonlinear parabolic equation  u   t  \u00a0=\u00a0\u2207( a ( u ) b ( x ) c ( t )\u2207 u )\u00a0+\u00a0 f ( x ,\u00a0 u ,\u00a0 q ,\u00a0 t ) with different kinds of boundary conditions. The upper bounds of the \u201cblow-up time\u201d and the \u201cupper estimates\u201d of global solutions are provided. Finally, some examples are presented as the application of the obtained results."}]