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Question: Incorrect Result from pdsolve for Diffusion IBVP (Invalid According to pdetest)

Question:Incorrect Result from pdsolve for Diffusion IBVP (Invalid According to pdetest)

Test007 50 Maple 2020
pde pdsolve differential-equations
June 12 2020
2

I want to solve the following IBVP:

However, the answer given by pdsolve doesn't give [0,0,0] with pdetest.


 

> 

restart
> 

eq := diff(u(x, t), t)-k*(diff(u(x, t), x, x)) = 0

diff(u(x, t), t)-k*(diff(diff(u(x, t), x), x)) = 0

 (1)
> 

ic := u(x, 0) = 0

u(x, 0) = 0

 (2)
> 

bc := u(0, t) = p(t)

u(0, t) = p(t)

 (3)
> 

sol := `assuming`([simplify(pdsolve([eq, ic, bc]))], [k > 0, x > 0, t > 0])

u(x, t) = (1/2)*x*(Int(p(zeta)*exp(-(1/4)*x^2/(k*(t-zeta)))/(t-zeta)^(3/2), zeta = 0 .. t))/(Pi^(1/2)*k^(1/2))

 (4)
> 

`assuming`([simplify(pdetest(sol, [eq, ic, bc]))], [k > 0, t > 0, x > 0])

[(1/2)*x*(-t*(Int(p(zeta)*exp(-(1/4)*x^2/(k*(t-zeta)))/(t-zeta)^(7/2), zeta = 0 .. t))+limit(p(zeta)*exp(-(1/4)*x^2/(k*(t-zeta)))/(t-zeta)^(3/2), zeta = t)+Int(p(zeta)*exp(-(1/4)*x^2/(k*(t-zeta)))*zeta/(t-zeta)^(7/2), zeta = 0 .. t)+Int(p(zeta)*exp(-(1/4)*x^2/(k*(t-zeta)))/(t-zeta)^(5/2), zeta = 0 .. t))/(Pi^(1/2)*k^(1/2)), 0, -p(t)]

 (5)
> 

``

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