GATE XE (Engineering Sciences) 2025 - Question 21

Section: Engineering Mathematics | Type: NAT | Marks: 2

Let 𝑢(𝑥, 𝑡) be the solution of the initial boundary value problem 𝜕𝑢 𝜕𝑡−𝜕2𝑢 𝜕𝑥2 −𝑢= 0, 0 < 𝑥< 𝜋, 𝑡> 0, 𝑢(𝑥, 0) = 2 sin (3𝑥 2 ) cos (𝑥 2) , 0 < 𝑥< 𝜋, 𝑢(0, 𝑡) = 𝑢(𝜋, 𝑡) = 0, 𝑡> 0. Then the value of lim 𝑡→∞𝑢( 3𝜋 4 , 𝑡) is equal to (rounded off to two decimal places)___________

Answer: 0.68 to 0.73