Regular solutions of transmission and interaction problems for wave equations

摘要

AbstractConsidernbounded domains Ω ⊆ ℝ k iand elliptic formally symmetric differential operatorsA1of second order on ΩiChoose any closed subspaceVindocumentclass{article}pagestyle{empty}begin{document}$ prodlimits_{i = 1}^n {L^2 left({Omega _i } right)} $end{document}, and extend (Ai)i=1,…,nby Friedrich's theorem to a self‐adjoint operatorAwithD(A1/2) =V(interaction operator). We give asymptotic estimates for the eigenvalues ofAand consider wave equations with interaction.With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32We also treat non‐linear interaction, using a the