       Re: Other PDE heat equation

• To: mathgroup at smc.vnet.net
• Subject: [mg79709] Re: Other PDE heat equation
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Thu, 2 Aug 2007 03:53:24 -0400 (EDT)
• Organization: Uni Leipzig
• References: <f8pkd4\$2vr\$1@smc.vnet.net>

```Hi,

for you second order equation you have two drgrees of freedom in
thr space direction, i.e., you can give (u[-L,t] and u[L,t]) or
(u[-L,t] and D[u[x,t,x]/. x->L) or (D[u[x,t,x]/. x->-L and u[L,t])
but you can't give three conditions, espcial not for inner points.
In the inner points of the interval the differential equation rules and
not any condition.

But you can solve the equation on the interval x in [0,L] and use
the symmetry of your equation (and the solution).

Regards
Jens

Miguel wrote:
> How can I to resolve the unidirectional heat transmission for a plate
> o slab:
>
> a=0.03;hc=1890;k=34;L=0.03;
>
> NDSolve[{a D[u[x,t],{x,2}]==D[u[x,t],t],
> u[L,0]==600,  (* Initial value: the plate has the same temperature *)
> u[-L,0]==600,
> u[0,0]==600,
> (D[u[x,t],x]/.x->0)==0  (* Max. in centre *)
> (D[u[x,t],x]/.x->L)==(-hc/k)(u[L,t]-600)    (* Q convection = Q
> conduction *)
> u[L,t]==u[-L,t]},  (* Temper. symetric *)
> u[x,t],{x,-L,L},{t,0,10}]
>
> NDSolve::ivone: Boundary values may only be specified for one \
> independent variable. Initial values may only be specified at one \
> value of the other independent variable. >>
>
> Where is my error?
>
> Thanks
>
>

```

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