In this paper, we use a functional analysis approach to prove the well-posedness for a parabolic system with a boundary Neumann condition and a nonlocal integral condition. The last step, is to establish the density of the range R(L) in the Hilbert space H, and hence the existence of a strong solution of the problem. The proof is mainly based on some a priori bounds and on some density arguments.
Digital Object Identifier (DOI)
Mecheri, Hacene and Rebiai, Belgacem
"A Mixed Problem with Integral Condition for a Parabolic System,"
Applied Mathematics & Information Sciences: Vol. 12
, Article 3.
Available at: https://dc.naturalspublishing.com/amis/vol12/iss4/3