6533b857fe1ef96bd12b4ce1

RESEARCH PRODUCT

Regular solutions of transmission and interaction problems for wave equations

E. MeisterFelix Ali Mehmeti

subject

Pure mathematicsOperator (computer programming)Transmission (telecommunications)General MathematicsBounded functionMathematical analysisGeneral EngineeringOrder (group theory)Differential operatorWave equationEigenvalues and eigenvectorsSubspace topologyMathematics

description

Consider n bounded domains Ω ⊆ ℝ and elliptic formally symmetric differential operators A1 of second order on Ωi Choose any closed subspace V in , and extend (Ai)i=1,…,n by Friedrich's theorem to a self-adjoint operator A with D(A1/2) = 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 Minty29.

yearjournalcountryeditionlanguage
1989-09-01Mathematical Methods in the Applied Sciences
https://doi.org/10.1002/mma.1670110507