Solve nonlinear numerical differential equations with several variables?

Questions
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1

Dear Wolfram community,

I have a nonlinear system with two variables. For Example:

Clear["Global`*"]
system = {
   D[a[t, x], t] == a[t, x] + b[t, x], 
   D[b[t, x], x] == a[t, x] b[t, x],
   a[t, 0] == 0.5, b[0, x] == 1};
solution = NDSolve[system, {a, b}, {t, 0, 10}, {x, 0, 10}]

and get as an error massgae:

NDSolve::femnonlinear: Nonlinear coefficients are not supported in this version of NDSolve..

What is my problem and my miss understanding?

Thank for your help.

2

What version are you running? It works on V12.

3

With version Mathematica 12.0 works fine.

9838Bez tytułu.png
9838Bez tytułu.png1425×802 250 KB

4

I use the version Mathematica 11.3.

Thank for your help.

Now, its work with Mathematica 12.0