Solve the diffusion equation with constant dissipation

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Reference no: EM133029901

Questions -

Q1. Solve the diffusion equation with constant dissipation:

u_t - ku_xx + bu = 0 for -∞ < x < ∞ with u(x, 0) = φ(x),

where b > 0 is a constant. (Hint: Make the change of variable u(x, t) = e^-btv(x, t).)

Q2. Solve the diffusion equation with variable dissipation:

u_t - ku_xx + bt²u = 0 for -∞ < x < ∞ with u(x, 0) = φ(x), where b > 0 is a constant.

Q3. Solve the heat equation with convection:

u_t - ku_xx + Vu_x= 0 for -∞ < x < ∞ with u(x, 0) = φ(x), where V is a constant.

Reference no: EM133029901

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