ASYMPTOTIC BEHAVIOR OF THE NON-AUTONOMOUS REACTION-DIFFUSION EQUATION WITH ROBIN BOUNDARY CONDITION


ÖZTÜRK E.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.68, ss.422-440, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 68 Konu: 1
  • Basım Tarihi: 2019
  • Doi Numarası: 10.31801/cfsuasmas.425500
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.422-440

Özet

In this paper, we investigate the long-time behavior of the timedependent reaction-diffusion equation ut-Delta u+a(x)vertical bar u vertical bar(rho) u-b(x)vertical bar u vertical bar(nu)u - h(x, t) with Robin boundary condition. We begin this paper with the existence and uniqueness results of the solution to the problem. For the asymptotic behavior, we.rstly prove the existence of an absorbing set in W-2(1) (Omega) boolean AND L rho+2(Omega). The existence of a uniform attractor is obtained in W-2(1) (Omega) boolean AND L rho+2(Omega).