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Question: pdes 1 consider the 1d beat diffusion equation applied to...

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PDEs. 1. Consider the 1D beat (diffusion) equation, applied to a bar of metal with 0SsL Start with a solution of the 6orm (a) Consider boandary conditions (BCs) such that the ends of the bar are at always at zeto temperature and the initial proile of the temperature is given by a funmction u(r,0)-) Show that a general form of the solution with these BCs can be expressed as a sum: Write down an expeession foe the B, in terns of fr). (b) What if the ends are not held at T-0 but rather they are insulated so no heat flows, in which case the spatial gradient of u at the ends are zero at all times (1) Show that for this case the general solution is a series where () Derive the solution for A and A in the case where the initial shape f(a) is triangalar
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