2.5.4 \(u_t + u u_x + \mu u_{xx}\) with IC

problem number 94

From Mathematica symbolic PDE document.

Viscous fluid flow with initial conditions.

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

With initial conditions

\(u\left ( x,0\right ) =\left \{ \begin {array} [c]{ccc}1 & & x< 0 \\ 0 & & x \geq 0 \end {array} \right . \)

Mathematica


\[\left \{\left \{u(x,t)\to \frac {1}{\frac {e^{-\frac {t-2 x}{4 \mu }} \left (\text {erf}\left (\frac {x}{2 \sqrt {\mu } \sqrt {t}}\right )+1\right )}{\text {erf}\left (\frac {t-x}{2 \sqrt {\mu } \sqrt {t}}\right )+1}+1}\right \}\right \}\]

Maple


sol=()

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