Partial Differential Equations — CSIR Net PYQ (Question 2)

Question

Let f(x,t) be a solution of the heat equation \frac{\partial f}{\partial t}=D\frac{{\partial }^{2}f}{\partial {x}^{2}} in one dimension. The initial condition at t=0 is f(x,0)={e}^{- {x}^{2}} for - \infty <x<\infty. Then for all t>0,f(x,t) is given by [Useful integral: \int_{- \infty }^{\infty } dx{e}^{- \alpha {x}^{2}}=\sqrt{\pi /\alpha }.]

Accepted Answer

Option 3

Partial Differential Equations — CSIR Net PYQ (Question 2)

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