Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610206 | Journal of Differential Equations | 2015 | 37 Pages |
Abstract
Some transmission problems are set in bodies with a crown of small thickness ε>0ε>0. For instance, those concerning the conductivity in the biological cell. By a natural change of variables, we transform them in transmission problems set in two cylindrical bodies ]−∞,0[×]−π,π[]−∞,0[×]−π,π[ and ]0,δ[×]−π,π[]0,δ[×]−π,π[ (where δ=ln(1+ε)δ=ln(1+ε)) and then, in some general elliptic abstract differential equations (Pδ)δ>0(Pδ)δ>0. The goal of this work is to give a complete study of these problems (Pδ)δ>0(Pδ)δ>0 for every δ>0δ>0. Existence, uniqueness and maximal regularity results are obtained for the classical solutions essentially by using the semigroups theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Rabah Labbas, Keddour Lemrabet, Kheira Limam, Ahmed Medeghri, Maëlis Meisner,