Parabolic Equations with Robin Type Boundary Conditions in a Non-rectangular Domain
نویسنده
چکیده
In this article, we study the parabolic equation ∂tu−c(t)∂ xu = f in the non-necessarily rectangular domain Ω = {(t, x) ∈ R : 0 < t < T, φ1(t) < x < φ2(t)}. The boundary conditions are of Robin type, while the right-hand side lies in the Lebesgue space L2(Ω). Our aim is to find conditions on c and the functions (φi)i=1,2 such that the solution belongs to the anisotropic Sobolev space H1,2(Ω) = {u ∈ L2(Ω) : ∂tu, ∂xu, ∂2 xu ∈ L2(Ω)}. For goal we use the method of approximation of domains.
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