Solve the boundary-value problem 02 u 0x2 0u 0t , 0 , x , 1, t . 0 u(0, t) u0, 0u 0x `
Chapter 13, Problem 15(choose chapter or problem)
Solve the boundary-value problem
\(\frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial u}{\partial t}\), 0<x<1, t>0
\(u(0, t)=u_{0}\), \(\left.\quad \frac{\partial u}{\partial x}\right|_{x=1}=-u(1, t)+u_{1}\), t>0
\(u(x, 0)=u_{0}\), 0<x<1
where \(u_{0}\) and \(u_{1}\) are constants.
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