Rajib Haloi, Dhirendra Bahuguna, Dwijendra N. Pandey
Abstract:
We prove the existence and uniqueness of a local
solution to a quasi-linear differential equation of parabolic type
with deviated argument in an arbitrary Banach space. The results are
obtained by applying the Sobolevskii-Tanabe theory of parabolic
equations, fractional powers of operators, and the Banach fixed point
theorem. We include an example that illustrates the
theory.
Submitted August 15, 2011. Published January 17, 2012.
Math Subject Classifications: 34G20, 34K30, 35K90, 47N20.
Key Words: Analytic semigroup; parabolic equation;
deviated argument; Banach fixed point theorem.
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Rajib Haloi Department of Mathematics and Statistics Indian Institute of Technology Kanpur Pin 208016, India Tel. +91-512-2597053, Fax +91-512-2597500 email: rajib.haloi@gmail.com |
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Dhirendra Bahuguna Department of Mathematics and Statistics Indian Institute of Technology Kanpur Pin 208016, India email: dhiren@iitk.ac.in |
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Dwijendra N. Pandey Department of Mathematics Indian Institute of Technology Roorkee Pin 247667, India email: dwij.iitk@gmail.com |
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