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Question

The one dimensional heat conduction partial differential equation Tt=2Tx2 is

A
Parabolic
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B
Hyperbolic
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C
Elliptic
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D
Mixed
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Solution

The correct option is A Parabolic
The general form of 2nd order partial differential equation is:
A2Ux2+B2Uxy+C2Uy2+f(x,y,u,Ux,Uy)=0 .... (i)
Tt=2Tx21.2Tx2+0.2TxY+0.2TY2+Tt=0
On comparision, A=1,B=0,C=0
B24AC=04(1)(0)=0
Given equatin is parabolic.

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