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Let u be the unique solution of

ut=2ux2 where (x,t)(0,1)×(0,)u(x,0)=sinπx,x(0,1)u(0,t)=u(1,t)=0,t(0,)}

Then which of the following is true?

1. There exists (x,t)(0,1)×(0,) such that u(x,t)=0

2. There exists (x,t)(0,1)×(0,) such that ut(x,t)=0

3. The function etu(x,t) is bounded for (x,t)(0,1)×(0,)

4. There exists (x,t)(0,1)×(0,) such that u(x,t)>1
in Differential Equation by Expert | 825 views

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