A Note on Evolution Equation on Manifold

Ashyralyev A. Sozen Y. Hezenci F.
2021 University of Nis

Filomat
2021 #35 Issue 15 5031 - 5043 pp.

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 Hölder spaces. Furthermore, in various Hölder 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.

Differential equations on manifolds , Self-adjoint positive definite operator , Well-posedness

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Department of Mathematics, Bahcesehir University, Istanbul, 34353, Turkey
Peoples’ Friendship University of Russia (RUDN University), Ul Miklukho Maklaya 6, Moscow, 117198, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Hacettepe University, Department of Mathematics, Ankara, 06800, Turkey
Duzce University, Department of Mathematics, Duzce, 81620, Turkey

Department of Mathematics
Peoples’ Friendship University of Russia (RUDN University)
Institute of Mathematics and Mathematical Modeling
Hacettepe University
Duzce University

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