我这个应该属于一个二阶偏微分方程组，二维（t，x）,13个方程13个变量
NDSolve[{
D[\[Sigma][t, x], t, t] - (1/t^2)*D[\[Sigma][t, x], x, x] + (1/t)*
D[\[Sigma][t, x], t] +
D[\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]], \[Sigma][t, x]] ==
0, (* Subscript[
D, \[Mu]]D^\[Mu]\[Sigma]+\[Delta]\[CapitalOmega]/\[Delta]\[Sigma]=
0 *)
t\[Sigma]tt[t, x] ==
D[\[Sigma][t, x], t]*
D[\[Sigma][t, x],
t] - ((1/2)*(D[\[Sigma][t, x], t]*D[\[Sigma][t, x], t] +
D[\[Sigma][t, x], x]*-D[\[Sigma][t, x], x]/(t^2)) -
u[\[Sigma][t, x]]), (* Subscript[
T, \[Sigma]]^\[Mu]\[Nu]=\[PartialD]^\[Mu]\[Sigma]\[PartialD]^\[Nu]\
\[Sigma]-(1/2(\[PartialD]\[Sigma])^2-U(\[Sigma]))g^\[Mu]\[Nu] *)
t\[Sigma]tx[t, x] ==
D[\[Sigma][t, x],
t]*-D[\[Sigma][t, x],
x]/(t^2), \
t\[Sigma]xt[t, x] == t\[Sigma]tx[t, x],
t\[Sigma]xx[t,
x] == -(D[\[Sigma][t, x], x]/(t^2))*-(D[\[Sigma][t, x],
x]/(t^2)) - ((1/
2)*(D[\[Sigma][t, x], t]*D[\[Sigma][t, x], t] +
D[\[Sigma][t, x], x]*-D[\[Sigma][t, x], x]/(t^2)) -
u[\[Sigma][t, x]])*(-1/t^2),
D[tqtt[t, x], t] + D[t\[Sigma]tt[t, x], t] + D[tqxt[t, x], x] +
tqtt[t, x]/t + t*tqxx[t, x] + D[t\[Sigma]xt[t, x], x] +
t\[Sigma]tt[t, x]/t + t*t\[Sigma]xx[t, x] ==
0, (* Subscript[D, \[Mu]](Subscript[T,
q]^\[Mu]\[Nu]+Subscript[T, \[Sigma]]^\[Mu]\[Nu])=0 *)
D[tqtx[t, x], t] + tqtx[t, x]/t + D[t\[Sigma]tx[t, x], t] +
t\[Sigma]tx[t, x]/t + D[tqxx[t, x], x] + 2*tqtx[t, x]/t +
D[t\[Sigma]xx[t, x], x] + 2*t\[Sigma]tx[t, x]/t == 0,
tqtx[t, x] == tqxt[t, x],
tqtt[t,
x] == (e[t,
x] - (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]))*ut[t, x]*
ut[t, x] + (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]), (*
Subscript[T, q]^\[Mu]\[Nu]=(\[Epsilon]+p)u^\[Mu]u^\[Nu]-
p g^\[Mu]\[Nu] *)
tqtx[t,
x] == (e[t,
x] - (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]))*ut[t, x]*ux[t, x],
tqxx[t,
x] == (e[t,
x] - (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]))*ux[t, x]*
ux[t, x] + (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]])*(-1/t^2),
ut[t, x]*ut[t, x] + ux[t, x]*ux[t, x]*(-(t^2)) ==
1, \
\
\
(* u^2=1 *)
e[t, x] ==
tt[t, x]*
D[-(\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]),
tt[t, x]] + (\[CapitalOmega]q[\[Sigma][t, x], tt[t, x], 0] +
u[\[Sigma][t, x]]) +
u[\[Sigma][t,
x]], (*
e=T\!\(
\*SubscriptBox[\(\[PartialD]\), \(T\)]p\)-p+U *)
tt[1, x] == (171/200)*Exp[-(x^2)/2],
tt[t, 10] == (171/200)*Exp[-(10^2)/2],
\[Sigma][t, 10] == 94/200,
\[Sigma][1, x] == (94/200)*
Exp[-((x -
10)^2)/(-33.5004)], \
(*see test.nb*)
\[Sigma][10, x] == 94/200,
Derivative[0, 1][\[Sigma]][t, 0] == 0
}, {\[Sigma], tt, t\[Sigma]tt, t\[Sigma]tx, t\[Sigma]xt,
t\[Sigma]xx, tqtx, tqtt, tqxt, tqxx, ut, ux, e}, {t, 1, 10}, {x, 0,
10}]
这里代码没有贴完全，里面的Ω在之前已经定义了

顶

顶。。

属于***了的问题