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Wave equation with second – order non – standard dynamical boundary conditions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Vázquez, Juan Luis |
| Copyright Year | 2008 |
| Abstract | The paper deals with the well–posedness of the problem 8 >< >: utt −∆u = 0 in R× Ω, utt = kuν on R× Γ, u(0, x) = u0(x), ut(0, x) = v0(x) in Ω, where u = u(t, x), t ∈ R, x ∈ Ω, ∆ = ∆x denotes the Laplacian operator respect to the space variable, Ω is a bounded regular (C∞) open domain of RN (N ≥ 1), Γ = ∂Ω, ν is the outward normal to Ω, k is a constant. We prove that it is ill–posed if N ≥ 2, while it is well–posed when N = 1. In the one dimensional case we give a complete existence, uniqueness and regularity theory. We also give some existence result for regular initial data when N ≥ 2 and Ω is a ball. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.uam.es/personal_pdi/ciencias/jvazquez/vazvit%20wave%20M3AS%2027-03-2008.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | BALL project Dynamical system Emoticon Well-posed problem Whole Earth 'Lectronic Link |
| Content Type | Text |
| Resource Type | Article |
