# differential equations – coupled pde with second-order spatial derivative

I'm trying to solve a PDE system using NDsolve but the following errors come with it.

NDSolveValue :: femcmsd: The spatial derivative order of the EDP can not
exceed two.

equations:

Qm and Q are constant.

``````                pde1 = {
re[qr[r, x, t], t]+ tq * D[RE[D[RÉ[D[qr[r, x, t], t], t]==
alpha * D[(1/r)*(D[r*qr[r, x, t], r]+ D[r*qx[r, x, t], X]), r]+
alpha * ta *
re[RE[D[RÉ[D[(1/r)*(D[r*qr[r, x, t], r]+ D[r*qx[r, x, t], X]), r], t]+
alpha * wrc * D[Te[r, x, t], r]+ alpha * wrc * ta * D[RE[D[RÉ[D[Te[r, x, t], t], r]};

pde2 = {
re[qx[r, x, t], t]+ tq * D[RE[D[RÉ[D[qx[r, x, t], t], t]==
alpha * D[(1/r)*(D[r*qr[r, x, t], r]+ D[r*qx[r, x, t], X]), X]+
alpha * ta *
re[RE[D[RÉ[D[(1/r)*(D[r*qr[r, x, t], r]+ D[r*qx[r, x, t], X]), X], t]+
alpha * wrc * D[Te[r, x, t], X]+ alpha * wrc * ta * D[RE[D[RÉ[D[Te[r, x, t], t], X]};

pde3 = {
ro * c * d[Te[r, x, t],
t]== - (1 / r) * (D[r*qr[r, x, t], r]+ D[r*qx[r, x, t], X]+
wrc * (Tb - Te[r, x, t]) + Qm
};

sol = NDSolveValue[{pde1, pde2, pde3, BC1, BC2, BC3, BC4, BC5, IC1,
IC2, IC3, IC4, IC5, IC6},
You[r, x, t], {t, 0, 5}, {r, x} [Element] [CapitalOmega]];
``````

Is it possible to handle this error?