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Search: MSC category 35K57 ( Reaction-diffusion equations )

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1. CJM 2009 (vol 62 pp. 74)

Ducrot, Arnaud; Liu, Zhihua; Magal, Pierre
Projectors on the Generalized Eigenspaces for Neutral Functional Differential Equations in $L^{p}$ Spaces
We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in $L^{p}$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.

Keywords:neutral functional differential equations, semi-linear problem, integrated semigroup, spectrum, projectors
Categories:34K05, 35K57, 47A56, 47H20

2. CJM 1997 (vol 49 pp. 798)

Yu, Minqi; Lian, Xiting
Boundedness of solutions of parabolic equations with anisotropic growth conditions
In this paper, we consider the parabolic equation with anisotropic growth conditions, and obtain some criteria on boundedness of solutions, which generalize the corresponding results for the isotropic case.

Keywords:Parabolic equation, anisotropic growth conditions, generalized, solution, boundness
Categories:35K57, 35K99.

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