Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 13, pp. 1-10.
Title: Existence and uniqueness of solutions for quasi-linear
differential equations with deviating arguments
Authors: Rajib Haloi (Indian Institute of Technology Kanpur, India)
Dhirendra Bahuguna (Indian Institute of Technology Kanpur, India)
Dwijendra N. Pandey (Indian Institute of Technology Roorkee, India)
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.