partial differential equations – How to find solve for second order pde with initial conditions using mathematica?


I have next task:
$$
frac{partial^2 u}{partial x partial y} = 0,~ u(x,x^2) = 0,~ frac{partial u}{partial x}(x, x^2) = sqrt{|x|},~|x| < 1
$$

I write this, but it don’t work:

weqn = D(u(x,y),x,y) == 0 
ic = {u(x,x^2) == 0, Derivative(0,1)(u)(x,x^2) == Sqrt(Abs(x)), Abs(x) < 1} 
sol = DSolve({weqn, ic},u,{x,y})

And I got next error:

DSolve: Equation or list of equations expected instead of Abs(x)<1 in the first argument {$mathrm u^{(1,1)}(x,y) == 0$, {$mathrm{u(x,x^2) == 0, u^{(0,1)}(x,x^2)==sqrt{Abs(x)},~ Abs(x)<1}$}}.

When I try to find a solution to a similar problem, when in conditionals the second argument like $ mathrm x ^ 2 $, I can’t do it.

Where did I go wrong?