Gfyuki

1 $begingroup$ I am trying to solve following coupled PDEs: I am not sure about suitable BCs. ClearAll[V, Rho, T] gamma = 5/3; ep = 0.05; d = 0.01; L = 1; H = 1.1; gpara = 0.38; System = {D[V[x, t],t] == -1/gamma/exp[-x/H]*{D[Rho[x, t], x] + D[T[x, t],x]} + Rho[x, t]/exp[-x/H]*gpara + 1.3*ep*D[V[x, t], {x, 2}], D[Rho[x, t], t] == - D[{exp[-x/H]*V[x, t]}, x], D[T[x, t], t] == D[{exp[-x/H]*V[x, t]}, x] - V[x, t]*Rho[x, t]*gpara - gamma*exp[-x/H]*D[V[x, t], x] + gamma*d*D[T[x, t], {x, 2}], V[x, t] == 0 /. x -> 0, V[x, t] == 0 /. x -> 1, Rho[x, t] == 0 /. x -> 0, Rho[x, t] == 0 /. x -> 1, T[x, t] == 0 /. x -> 0, T[x, t] == 0 /. x -> 1, D[T[x, t], x] == 0 /. x -> 1, V[x, 0] == Sin[Pi*x/L], Rho[x, 0] == 0, T[x, 0] == 0}; {V, Rho, T} = NDSolveValue[System, {V, Rho, T}, {x, 0,