2.5.3 \(u_t+ u u_x = \mu u_{xx}\)

problem number 93

From Mathematica symbolic PDE document.

viscous fluid flow with no initial conditions

Solve for \(u(x,t)\) \[ u_t+ u u_x = \mu u_{xx} \]

Mathematica


\[\left \{\left \{u(x,t)\to -2 c_1 \mu \tanh (c_2 t+c_1 x+c_3)-\frac {c_2}{c_1}\right \}\right \}\]

Maple


\[u \left (x , t\right ) = \frac {-2 c_{2}^{2} \mu \tanh \left (c_{3} t +c_{2} x +c_{1}\right )-c_{3}}{c_{2}}\]

________________________________________________________________________________________