Question

the laplace equation in two dimensions is
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Answer 1

Answer:

We will essentially just consider a specific case of Laplace's equation in two dimensions, for the system with the boundary conditions shown in Fig. ... We will see that at steady-state (i.e., no time dependence) the diffusion equation reduces to the Laplace's equation.

Hope it helps..

Answer 2

Answer:

Laplace equation in 2 dimension is $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0$

Step-by-step explanation:

• Laplace equation is a second degree partial differential equation.
• It can be written in # dimension as $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} =0$

     where x, y, z are the 3 dimension.

• In 2 dimension only x, y variable exists. Thus the equation becomes

          $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} =0$