Geodesic
Existence of solution for parabolic equation with non-power nonlinearities
Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 31-47

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We consider the first mixed problem for a class of parabolic equation with double non-exponential nonlinearities in a cylindrical domain $D=(t>0)\times\Omega$. By Galerkin's approximations we prove the existence of strong solutions in Sobolev–Orlich space.
Keywords: $N$-functions, Sobolev–Orlich spaces.
Mots-clés : parabolic equation, existence of solution 
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E. R. Andriyanova; F. Kh. Mukminov. Existence of solution for parabolic equation with non-power nonlinearities. Ufa mathematical journal, Tome 6 (2014) no. 4, pp. 31-47. http://geodesic.mathdoc.fr/item/UFA_2014_6_4_a2/