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A hybrid system of PDE’s arising in multi-structure interaction: coupling of wave equations in \(n\) and \(n-1\) space dimensions. (English) Zbl 1108.35110
Vázquez, Juan Luis (ed.) et al., Recent trends in partial differential equations. UIMP-RSME Santaló summer school, Santander, Spain, July 12–16, 2004. Providence, RI: American Mathematical Society (AMS); Madrid: Real Sociedad Matemática Española (ISBN 0-8218-3891-1/pbk). Contemporary Mathematics 409, 55-77 (2006).
In the paper the authors analyse the fine properties of a model arising in multi-body or built-up structures constituted by two \(n\)-dimensional wave equations coupled with a \((n-1)\)-dimensional one along a flexible interface. When \(n=2\) this system models the coupling of two 2-d wave equations through a 1-d elastic string. The material properties (such as rigidity, density and velocity of propagation of waves) in each of the three media (the two \(n\)-dimensional domains and the interface) do not need to be the same.
For the entire collection see [Zbl 1094.35001].

35L55 Higher-order hyperbolic systems
35A21 Singularity in context of PDEs