Hello, please I tried to solve this system by NDSolve, but I find errors and I do not know why! if someone can help me? Thank you
t1 = 2;
(Définit la fonction indicatrice)
indicator[x_] := Piecewise[{{1, 0 < x < 1/2}}, 0];
E1 = D[g[x, t], {x, 2}] - D[g[x, t], {t, 2}] == indicator[x]*((Cos[\[Pi] t1] - Sin[\[Pi] t1]) Sin[\[Pi] x])/(
4 \[Pi])*DiracDelta[t - t1];
ic = {g[x, 0] == Sum[Sin[k *\[Pi]*x], {k, 1}], Derivative[0, 1][g][x, 0] == Sum[k *\[Pi] *Sin[k *\[Pi]* x], {k, 1}]};
(*Condition aux bord de Dirichlet*)
bcc = {g[0, t] == 0, g[1, t] == 0};
(*résolution numérique de l'équation*)
sol11 = NDSolve[{E1, ic, bcc}, g, {x, 0, 1}, {t, 0, 12}, MaxStepSize -> 0.1];
Best regards,