Existence of solutions in the alpha-norm for partial differential equations of neutral type with finite delay
ABSTRACT 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.
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ABSTRACT: We study the existence, regularity and stability of solutions for some nonlinear class of partial neutral functional differential equations. We assume that the linear part generates a compact analytic semigroup on a Banach space X, the delayed part is assumed to be continuous with respect to the fractional power of the generator. For illustration, some application is provided for some model with diffusion and nonlinearity in the gradient.03/2013; 15(1):49-75. DOI:10.4067/S0719-06462013000100004