heat equation

[mona123]

I want to know if the solution of heat equation verifies the estimate
0<u(t,x)<||u0||∞,(where u₀ is the initil data u(0,x)) then this estimate is sufficient to prove that the maximum time of existance of u is infinity.Can someone help?

 

[Ishuda]

I want to know if the solution of heat equation verifies the estimate
0<u(t,x)<||u0||∞,(where u₀ is the initil data u(0,x)) then this estimate is sufficient to prove that the maximum time of existance of u is infinity.Can someone help?

What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/threads/78006-Read-Before-Posting


I'm not sure of your question [I'm not sure of the 0<u(t,x)<||u0||∞ meaning]. I would assume the ||u0|| = ||u(0,x)|| is some sort of norm but what does the 'tacked on ∞' mean? Or do you possibly mean the ∞ norm which would generally be interpreted as the maximum of |u(0,x)| over the domain of x? In any case, we would also need to know if you are using the usual assumptions such no sources nor sinks, etc.?