Question: How I can solve these differential equations?

How I can solve these time delay  differential equations?

please see attatched files.

Best

Doc191.pdf

ny.mw

 


 

restart; d[1] := 1; d[2] := 4; d[3] := 1; r[1] := 1; r[2] := 1; r[3] := 1; r[4] := .5; a[11] := .5; a[12] := 3; a[21] := 2; a[22] := .8; a[23] := 1; a[32] := .5; a[33] := .9; tau := .3

diff(u(t, x), t) = d[1]*(diff(u(t, x), x, x))+u(t, x)*{r[1]-a[11]*u(t, x)-a[12]*v(t, x)}

diff(u(t, x), t) = diff(diff(u(t, x), x), x)+u(t, x)*{1-.5*u(t, x)-3*v(t, x)}

(1)

diff(v(t, x), t) = d[2]*(diff(v(t, x), x, x))+v(t, x)*{r[2]+a[21]*u(t-tau, x)-a[22]*v(t, x)-a[23]*w(t-tau, x)}

diff(v(t, x), t) = 4*(diff(diff(v(t, x), x), x))+v(t, x)*{1+2*u(t-.3, x)-.8*v(t, x)-w(t-.3, x)}

(2)

diff(w(t, x), t) = d[3]*(diff(w(t, x), x, x))+w(t, x)*{r[3]+a[32]*v(t, x)-a[33]*w(t, x)}

diff(w(t, x), t) = diff(diff(w(t, x), x), x)+w(t, x)*{1+.5*v(t, x)-.9*w(t, x)}

(3)

0 < x and x < Pi, t > 0

0 < x and x < Pi, 0 < t

(4)

diff(u(t, x), x) = 0, diff(v(t, x), x) = 0, diff(w(t, x), x) = 0, x = 0, x = Pi, t >= 0

diff(u(t, x), x) = 0, diff(v(t, x), x) = 0, diff(w(t, x), x) = 0, x = 0, x = Pi, 0 <= t

(5)

u(t, x) > 0, v(t, x) > 0, w(t, x) > 0, `in`(t, x, `&x`([-tau, 0], [0, Pi]))

0 < u(t, x), 0 < v(t, x), 0 < w(t, x), `in`(t, x, [-.3, 0]*[0, Pi])

(6)

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