निम्नलिखित द्वितीय-क्रम रैखिक आंशिक विभेदक समीकरणों (second-order linear PDEs) में से कौन सा दीर्घवृत्तीय (elliptic) है?

Let u(x, t) be the solution of the initial value problem: utt - uxx = e-t, x ∈ ℝ, t > 0, u(x, 0) = cos x, ut(x, 0) = 0, x ∈ ℝ. Then which of the following statements is true?

Consider the initial-boundary value problem (IBVP): ut + ux = 0, 0 0, u(x, 0) = ex, 0 0. Which of the following statements is true?