Turkish Journal of Mathematics
We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial differential equations (PDEs) in unbounded domains. The main attention is payed to elliptic boundary problems in general unbounded domains. In contrast to the previous works in this direction our theory does not require the underlying domain to be cylindrical or cone-like or to be shift semiinvariant with respect to some direction. In particular, the theory is applicable to the exterior domains.
Multiparametric semigroups, attractors, unbounded domains, elliptic PDEs, exterior domains
KOSTIANKO, ANNA and ZELIK, SERGEY
"Attractors for semigroups with multi-dimensional time and PDEs in unbounded domains,"
Turkish Journal of Mathematics: Vol. 47:
3, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss3/6