Question

The nature of one dimensional heat equation
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Answer 1

Answer:

Explanation: The one-dimensional heat equation is given by ut = c2uxx where c is the constant and ut represents the one time partial differentiation of u and uxx represents the double time partial differentiation of u. ... Therefore the constant should be negative, i.e., k = – p2.

Answer 2

Answer:

 The nature of the one dimensional heat equation is parabolic.

Step-by-step explanation:

Tip

• The heat equation is given by  $A \left\frac{\partial^2 u}{\partial x^2} + B\frac{\partial^2 u}{\partial xy} +C \frac{\partial^2 u}{\partial y^2} +D\left\frac{\partial u}{\partial x} +E\frac{\partial u}{\partial y} + Fu+G=0$
• The heat equation in 1 dimension is given by

         $\[ \frac{\partial T}{\partial t} = \alpha \left \frac{\partial^2 T}{\partial x^2}$

Step1 of 1:

• comparing two equations

     A=$\alpha$ , B=0,C=0

•  $D=B^{2}-4AC$

       D=0

• Thus, the heat equation is parabolic.