Electron. J. Diff. Equ., Vol. 2015 (2015), No. 64, pp. 1-9.

Nonlocal singular problem with integral condition for a second-order parabolic equation

Ahmed Lakhdar Marhoune, Ameur Memou

We prove the existence and uniqueness of a strong solution for a parabolic singular equation in which we combine Dirichlet with integral boundary conditions given only on parts of the boundary. The proof uses a priori estimate and the density of the range of the operator generated by the problem considered.

Submitted September 3, 2014. Published March 18, 2015.
Math Subject Classifications: 35B45, 35K67, 35K20.
Key Words: Energy inequality; integral boundary conditions; singular parabolic equation; strong solution.

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Ahmed Lakhdar Marhoune
Laboratoire Equations Differentielles
Departement de Mathematiques, Faculte des Sciences Exactes
Université des Fréres Mentouri
25000 Constantine, Algerie
email: ahmed_marhoune@hotmail.com
Ameur Memou
Departement de Mathematiques
Université de M'sila, Algerie
email: memoua_2007@yahoo.fr

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