
1352 LINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH MATHEMATICA
ic2=Map[LaplaceTransform[#,t,s]&,ic1,{2}] {eq3=(eq2/.ic1),
bc1=u[0,t]==a*f[t]}
bc2=LaplaceTransform[bc1,t,s]/.{LaplaceTransform[u[0,t],t,s]->u1[0],
LaplaceTransform[f[t],t,s]->f1[s]}
{sol=DSolve[eq3,u1[x],x], sol1=u1[x]/.sol}
l1=Limit[sol1[[1,1]],x->Infinity,Assumptions->{c>0,s>0}]//Simplify
l2=Limit[sol1[[1,2]],x->Infinity,Assumptions->{c>0,s>0}]//Simplify
{sol2=sol1/.{C[1]->0}, sol3=sol2/.{C[2]->bc2[[2]]}}
u2=sol3/.f1[s]->LaplaceTransform[f[t],t,s]
solF=InverseLaplaceTransform[u2,s,t]
23.3.3 Con structing Analytical Solutions in Terms of Green’s Functions
It is well known that the linear superpo ...