For u t−u xx=0,0 0, with u(x,0)=0,u(0,t)=1,u(2,t)=3, find the steady-state value at x=1.

GATE 2022 MA – Question 21

Partial Differential Equations · Heat and Wave Equations · 1 mark · Multiple choice

For u_t−u_xx=0,0<x<2,t>0, with u(x,0)=0,u(0,t)=1,u(2,t)=3, find the steady-state value at x=1.

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Correct answer: (B) 2

Steady state U satisfies U″=0, so U=ax+b. Endpoint values give b=1,a=1. Thus U(1)=**2, B**. The initial condition determines the decaying transient.

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