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EDP linéaire du premier ordre. L'équation de transport

22 pages
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a(x,t)u (x,t)+b(x,t)u (x,t)+c(x,t)u(x,t) =d(x,t)t x
2(x,t) ∈ Ω ⊂ IR t
nx∈ IR
a(x,t)u (x,t)+b(x,t).∇ u(x,t)+c(x,t)u(x,t) =d(x,t)t x
b(x.t)
au (x,t)+bu (x,t) = 0t x
b
a = 0 c =
a
u (x,t)+cu (x,t) = 0t x
t = 0
u(x,0) =φ(x),
t
u(x,t) =φ(x−ct)
z =x−ct
∂φ∂(x−ct) dφ
u (x,t) = =x
∂z ∂x dz
∂φ∂(x−ct) dφ
u (x,t) = =−ct
∂z ∂t dz
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