Prove that the Steady state solution of heat equation is unique

Introduction : Here we shall Prove that the Steady state solution of heat equation is unique. Question : Given heat equation \[u_t=u_{xx}\ \ ,\ 0<x<1,\ t>0 \] \[\ u\left(0,t\right)=0\ ,\ u\left(1,t\right)=\cos{\left(\omega t\right)},\ \ t>0\] \[u\left(x,0\right)=f\left(x\right)\ ,\ 0<x<1\] Prove that the…

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