How to solve non-linear second order Differential equations in 2 variables in Matlab?

These are my equations:

dT/dt=A1+A2*T+A3*T^4+A4*((dT1/dx)@x=0)........Eqn1

dT1/dt=B1*(d2T1/dx2) ..........Eqn2

Initial conditions: @t=0 T=To, T1=T1o for all x.

Boundary conditions: @x=0 T=T1, @x=xo T1=T11(const).

where T and T1 are two different variables. All coefficients are constants.

d2T1/dx2 means ddT1/ddx.

I found only examples of one variable till now. Any help on how to proceed or which solvers to use would be very appreciated. Thanks in advance!

[pietro]

there are infinitive solutions to this problem, so you can't solve the equation. You could use the optimization solver and set some constraints to the solution.

[siddhartha desu]

Thanks for the response. Can you tell me which solver to use, an example if available. Thanks in advance!