Tag Archives: Laplace

Solving a Convection PDE

The problem under consideration is a linear convection PDE.

\(\) From Farlow’s “Partial Differential Equations for Scientists and Engineers”, chapter 15 problem 3 is $$u_t = -2u_x \quad -\infty < x < \infty \quad 0<t<\infty $$$$ u(x,0)=e^{-x^2}$$

Intuition

We see that the governing equation is a linear convection problem. The characteristic velocity is 2. We expect the solution to be a shifted initial condition $$u(x,t)=e^{-(x-2t)^{2}}$$

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