Singular functional differential equations of neutral type in Banach spaces |
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Authors: | Said Hadd |
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Affiliation: | Department of Electrical Engineering and Electronics, The University of Liverpool, Brownlow Hill, L69 3GJ, Liverpool, United Kingdom |
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Abstract: | The well-posedness of a large class of singular partial differential equations of neutral type is discussed. Here the term singularity means that the difference operator of such equations is nonatomic at zero. This fact offers many difficulties in applying the usual methods of perturbation theory and Laplace transform technique and thus makes the study interesting. Our approach is new and it is based on functional analysis of semigroup of operators in an essential way, and allows us to introduce a new concept of solutions for such equations. Finally, we study the well-posedness of a singular reaction-diffusion equation of neutral type in weighted Lebesgue's spaces. |
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Keywords: | Neutral equations Nonatomic operators Semigroup Banach space |
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