Geodesic
Existence of solutions in the \(\alpha\)-norm for partial differential equations of neutral type with finite delay
Electronic journal of differential equations, Tome 2010 (2010)
In this work, we prove results on the local existence of mild solution and global continuation in the alpha-norm for some class of partial neutral differential equations. We suppose that the linear part generates a compact analytic semigroup. The nonlinear part is just assumed to be continuous. We use the compactness method, to show the main result of this work.
Classification : 34K30, 47D06
Keywords: neutral equation, analytic semigroup, fractional power, phase space, mild solution, sadovskii's fixed point theorem 
@article{EJDE_2010__2010__a79,
     author = {Ezzinbi,  Khalil and Megdiche,  Hatem and Rebey,  Amor},
     title = {Existence of solutions in the \(\alpha\)-norm for partial differential equations of neutral type with finite delay},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1214.34067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a79/}
}
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%F EJDE_2010__2010__a79
Ezzinbi,  Khalil; Megdiche,  Hatem; Rebey,  Amor. Existence of solutions in the \(\alpha\)-norm for partial differential equations of neutral type with finite delay. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a79/