PDE combined with ODE 1D

Question

I try to solve the following system of PDE coupled with ODE: $$\theta_t - a\theta_{xx} + b\kappa_a(\theta^4-\varphi)=0,$$ $$-\alpha\varphi_{xx} + \kappa_a(\varphi - \theta^4) = 0,$$ $$-a\theta_x + \beta\theta|_{x=0} = 0,\;\;a\theta_x + \beta\theta|_{x=L} = 0$$ $$-\alpha\varphi_x + \gamma\varphi|_{x=0} = 0,\;\;\alpha\varphi_x + \gamma\varphi|_{x=L} = 0$$ $$\theta|_{t=0} = \theta_0, \;\;\varphi_{t=0} = \varphi_0$$ for functions $\theta, \varphi$.

I use the following code ($\zeta = \theta - \theta_s$, $\xi = \varphi - \varphi_s$ where $\theta_s, \varphi_s$ is the solution of the stationary problem):

s = NDSolve[{D[zeta[t, x], t] - a*D[zeta[t, x], x, x] + 
 b*kappaa*(((thetas[x] + zeta[t, x])^4 - thetas[x]^4) - 
    xi[t, x]) == 0,
   -alpha*D[xi[t, x], x, x] + 
     kappaa*(xi[t, x] - ((thetas[x] + zeta[t, x])^4 - thetas[x]^4)) ==
     0,
   zeta[0, x] == zeta0[x], xi[0, x] == xi00[x],
   -a*Derivative[0, 1][zeta][t, 0] + beta*zeta[t, 0] == 0, 
   a*Derivative[0, 1][zeta][t, ll] + beta*zeta[t, ll] == 0,
   -alpha*Derivative[0, 1][xi][t, 0] + gamma*xi[t, 0] == 0,
   alpha*Derivative[0, 1][xi][t, ll] + gamma*xi[t, ll] == 0},
  {zeta, xi}, {x, 0, ll}, {t, 0, tt}]

The initial condition for $\theta$ is prescribed, the initial condition for $\varphi$ was computed.

Wolfram Mathematica doesn't solve this system.

How can I solve it?