Question

Partial Differential Equations: The following convection-diffusion-decay equation appears in many physical applications: ut = Duxx - cux - gu Show that this equation can be transformed into a heat equation for w(x,t) by applying the transformation u(x,t) = w(x,t)e^(ax-bt) HINT: You will only obtain a heat equation for w(x,t) with an appropriate choice for the constants a and b in terms of the constants D, c, and g. Determine the choice for a and b that produces a heat equation for w(x,t).

          Partial Differential Equations:
The following convection-diffusion-decay equation appears in many physical applications:
ut = Duxx - cux - gu
Show that this equation can be transformed into a heat equation for w(x,t) by applying the transformation
u(x,t) = w(x,t)e^(ax-bt)
HINT: You will only obtain a heat equation for w(x,t) with an appropriate choice for the constants a and b in terms of the constants D, c, and g. Determine the choice for a and b that produces a heat equation for w(x,t).

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