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Regular solutions of transmission and interaction problems for wave equations
Author(s) -
Mehmeti Felix Ali,
Meister E.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110507
Subject(s) - mathematics , bounded function , eigenvalues and eigenvectors , operator (biology) , order (exchange) , subspace topology , elliptic operator , pure mathematics , unbounded operator , partial differential equation , mathematical analysis , finite rank operator , banach space , economics , gene , biochemistry , chemistry , physics , finance , repressor , quantum mechanics , transcription factor
Consider n bounded domains Ω ⊆ ℝ k iand elliptic formally symmetric differential operators A 1 of second order on Ω i Choose any closed subspace V in \documentclass{article}\pagestyle{empty}\begin{document}$ \prod\limits_{i = 1}^n {L^2 \left({\Omega _i } \right)} $\end{document} , and extend ( A i ) i =1,…, n by Friedrich's theorem to a self‐adjoint operator A with D ( A 1/2 ) = V (interaction operator). We give asymptotic estimates for the eigenvalues of A and consider wave equations with interaction. With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces. 25,32 We also treat non‐linear interaction, using a theorem of Minty 29 .