u(x,t) defined for x>0 t>0(adsbygoogle = window.adsbygoogle || []).push({});

d2u/dx2=du/dt

Conditions:

u(x,0)=0

d/dx u(0,t)=-1

u(x,t) tends to 0 as x tends to infinity

d2v/dx2 =pv

d/dx v(0,p) =-1/p

v(x,p)=integral(0 to inf) exp(-pt) u(x,t) dt

How do we use this to find v(x,p) and u(0,t)?

For u(0,t) can we simply integrate wrt x d/dx u(0,t) = -x?

Thanks in advance

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# Homework Help: Heat equation

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