Let u(x,t) be the solution of the initial value problem utt-uxx=e^-t, xinR, t0,qquad u(x,0)=cos x, ut(x,0)=0, xinR . Then which of the following statements is true?

(C) For each x0inR, there exists a t00 such that u(x0,t0)ge4.

Q48Section B (Part B)48 of 120

Partial differential equations — a forced wave equation

Let $u(x,t)$ be the solution of the initial value problem

$u_{tt}-u_{xx}=e^{-t}, x\in\mathbb{R}, t>0,\qquad u(x,0)=\cos x, u_t(x,0)=0, x\in\mathbb{R} .$

Then which of the following statements is true?

Pick an option to check your answer.

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