TIME DEGENERATE NEUMANN INITIAL BOUNDARY VALUE PROBLEMS AND APPLICATIONS

Dhaigude R.M.¹*, Sandip M.², Patil Devkatte³, Bodkhe S.G.⁴*
¹Department of Mathematics, Arts, Science and Commerce College, Badnapur, 431202, MS
²Sandip Nivas, Vidhut Nagar, Nanded, 431602, MS
³Department of Mathematics, Arts, Science and Commerce College, Badnapur, 431202, MS
⁴Department of Statistics Arts, Science and Commerce College, Badnapur, 431202, MS, India
* Corresponding Author : sgbodkhe@gmail.com

Received : -     Accepted : -     Published : 15-06-2010
Volume : 2     Issue : 1       Pages : 84 - 88
Int J Mach Intell 2.1 (2010):84-88
DOI : http://dx.doi.org/10.9735/0975-2927.2.1.84-88

Keywords : Neumann IBVP, positivity Lemma, Upper and Lower solution, Monotone Property, Existence – comparison and uniqueness solutions
Conflict of Interest : None declared

The aim of this paper is to develop monotone method for nonlinear time degenerate parabolic Neumann initial boundary value problems. These Problems are important in the Study of Physics, Ecology, Heat and Mass Transfer and any other branches of science and Engineering. Monotone Method is one of the important method in the theory of differential equations The main idea of this method is to develop iterative scheme based on the notion of upper and lower solutions. Using upper and lower solutions as distinct initial iterations, two monotone sequences are constructed. It is shown that these two sequences converge monotonically from about and below to maximal and minimal solutions respectively which lead to the existence – comparison and uniqueness results for the solution of nonlinear time degenerate Neumann IBVP. Positivity lemma is also obtained which play an important role in the proofs of these results.

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