(*Initial Parameters*)Needs["NDSolve`FEM`"];
Mobi = 1.0; lame = 0.01; noise = 0.02; conu0 = 0.63;
xmax = 1.0;
ymax = 1.0;
tmax = 1.0;

[CapitalOmega] = Rectangle[{0, 0}, {a, b}] /. {a -> 1, b -> 1};
RegionPlot[[CapitalOmega], AspectRatio -> Automatic]
mesh = ToElementMesh[[CapitalOmega], "MaxCellMeasure" -> 1/1000,
   "MeshElementType" -> QuadElement];
mesh["Wireframe"]
n = Length[mesh["Coordinates"]]
u0 = ElementMeshInterpolation[{mesh},
   conu0 + noise*(0.5 - RandomReal[{0, 1}, n])];
Plot3D[u0[x, y], {x, y} [Element] mesh]

op1 = !(
*SubscriptBox[([PartialD]), (t)](u[t, x, y])) - !(
*SubsuperscriptBox[([Del]), ({x, y}), (2)](v[t, x, y]))*
   Mobi

op2 = v[t, x, y] -
  200 *u[t, x, y] (1 - 3 *u[t, x, y] + 2 *u[t, x, y]^2) + lame*!(
*SubsuperscriptBox[([Del]), ({x, y}), (2)](u[t, x, y]))

{unn, vnn} =
  NDSolve[{op1 == 0, op2 == 0, u[0, x, y] == u0[x, y],
    v[0, x, y] == 0}, {u, v}, {t, 0, tmax}, {x, y} [Element] mesh];