PDEMOC2

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Let $x=x(t)\,$ so $u=u(x(t),t)\,$ .

$u_t = u_x x'(t) + u_t = u_t + u u_x = 0\,$ so $u\,$ is constant with respect to $t\,$ and

$u(x(t),t) = u(x(0),0) = x_0\,$

$x'(t) = u\,$

$x(t) = ut+x_0\,$

Since $u(x,t) = x-ut\,$ , the solution is $u(x,t) = \frac{x}{1+t}, t>-1\,$ .

Main Page : Partial Differential Equations : Method of Characteristics

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