Open AccessA note on evolution equation on manifold
Author(s) -
Allaberen Ashyralyev,
Yaşar Sözen,
Fatih Hezenci
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2115031a
Subject(s) - mathematics , mathematical analysis , manifold (fluid mechanics) , boundary value problem , type (biology) , hyperbolic partial differential equation , boundary (topology) , partial differential equation , parabolic partial differential equation , mechanical engineering , ecology , engineering , biology
In the present paper, considering the differential equations on smooth closed manifolds, we investigate and establish the well-posedness of boundary value problems nonlocal type for parabolic equations and also hyperbolic equations in H?lder spaces. Furthermore, in various H?lder norms we establish new coercivity estimates for the solutions of such type parabolic boundary value problems on manifolds and hyperbolic boundary value problems on manifolds as well.