Monthly Archives: February 2012

The Semi-Homogeneous Heat Problem

In this lecture, we study how to solve the semi-homogeneous heat problem: $$ \begin{aligned} &u_t=\alpha^2 u_{xx}+F(x,t),\ 0<x<L,\ t>0\\ &{\rm BCs:}\ \left\{\begin{aligned} -k_1u_x(0,t)+h_1u(0,t)&=0,\ t>0\\ k_2u_x(L,t)+h_2u(L,t)&=0, \end{aligned} \right.\\ &{\rm IC:}\ u(x,0)=\phi(x),\ 0<x<L\ \ \ \ \ (1) \end{aligned} $$ We consider a … Continue reading

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