Question #24830

Consider the pde u_t + (4u^3 + 4u)u_x = 0.

a) Express the pde in conservation form: ∂/∂x[F(u)] = 0.

b) Consider a weak solution in the form of a shock wave: u = {u- if x < λ(t), u+ if x > λ(t)}

Find the speed of propagation λ'(t) of the shock wave.

a) Express the pde in conservation form: ∂/∂x[F(u)] = 0.

b) Consider a weak solution in the form of a shock wave: u = {u- if x < λ(t), u+ if x > λ(t)}

Find the speed of propagation λ'(t) of the shock wave.

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