Solve differential equation with Delay, please help!!

Questions
1

Good evening, Please I stuck in a programme of a differential equation with Delay
I want to solve the following equation:

T= 2,
homogen =  D[f[x, t], t] - D[f[x, t], {x, 2}]  +  Integrate[ t*s*Sin[t] (f[x, s - 1])^2, {s, 0, t}] 
+  (3 + Abs[f[x, t - 1]])/(40 Exp[t]* (1 + Abs[f[x, t - 1]]))  == 0;
(*données initiales propres *)
ic = {f[x, t /; t <= 0] == x^2  t^2};
(* Condition aux bord de Dirichlet*)
bc = {f[0, t] == 0, f[\[Pi], t] == 0};
(*résolution analytique de l'équation *)
sol1 = NDSolveValue[{homogen, ic, bc}, f, {x, 0, \[Pi]}, {t, -T, T}]
2

Your equations do not make sense to me. Your integration is in “s” but there are “s” variables in the rest of the expression. Also, you probably should give some background as to how the equations are derived to be of more help (and to help us determine if they are correct).

Regards,

Neil

3

Hello Neil, I just corrected the code, sorry I didn’t pay attention at the beginning, now it’s just a heat equation with delay. but I still can’t resolve it.

I think there is a problem in the initial conditions “ic”

Best regards,