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Question: Solving PDE IVP with inequalities in domains

Question:Solving PDE IVP with inequalities in domains

Test007 50 Maple
assumptions pde pdsolve differential-equations boundary-conditions
June 02 2020
1

I want to solve the following problem in Maple:

I used the following Maple code. I am unsure whether this is the correct way of entering the assumptions for the initial and boundary conditions though.


 

> 

eq := diff(u(x, t), t, t)-4*(diff(u(x, t), x, x)) = 0

diff(diff(u(x, t), t), t)-4*(diff(diff(u(x, t), x), x)) = 0

 (1)
> 

ic := `assuming`([u(x, 0) = 4*sin(x), (D[2](u))(x, 0) = 0], [x > 0])

u(x, 0) = 4*sin(x), (D[2](u))(x, 0) = 0

 (2)
> 

bc := `assuming`([(D[1](u))(0, t) = 0], [t > 0])

(D[1](u))(0, t) = 0

 (3)
> 

`assuming`([simplify(pdsolve([eq, ic, bc]))], [`and`(t > 0, x > -t)])

u(x, t) = (-4*Heaviside(x-2*t)+4)*sin(2*t-x)+4*sin(x)*cos(2*t)

 (4)
> 

``
> 

``

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