Session H Chair
Session V
Title: Degenerate Dispersive Equations
Abstract: We discuss recent work on some quasilinear toy models for the phenomenon of degenerate dispersion, where the dispersion relation may degenerate at a point in physical space. In particular, we discuss the stationary states, as well as existence and uniqueness of solutions for degenerate KdV and NLS-type equations using a novel change of variables. This is joint work with Pierre Germain and Ben Harrop-Griffiths. Given time, we will discuss some work on Gibbs measures for a discrete version of this problem that is joint with with Jonathan Mattingly and Dana Mendelson.

Title: Stability by Fixed Point Theory for Nonlinear Delay and Fractional Differential Equations
Abstract: In this paper we study the stability properties of nonlinear differential equations with variable delays and give conditions to ensure that the zero solution is asymptotically stable by applying Krasnoselskii’s Fixed Point Theorem. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The same technique is also applied to some nonlinear fractional differential equations of Caputo type.

Title: The Coupling Conduction Effects on Natural Convection Flow along a Vertical Flat Plate with Joule Heating and Heat Generation
Abstract: The out-turn of heat generation and Joule heating on natural convection flow through a vertical flat plate have been investigated in the given article. Joule heating and heat conduction due to wall thickness ‘b’ are esteemed as well in this analysis. With the intent to obtain similarity solutions to the problem being constituted, the evolved equations are made dimensionless employing appropriate transformations. The non-dimensional equations are then modified into non-linear equations by bringing into being a non-similarity transformation. The out-turn non-linear alike equations confine with their commensurate boundary conditions formed on conduction and convection are solved numerically applying the finite difference method accompanied by Newton’s linearization approximation. The numerical outcomes in terms of the skin friction coefficient, velocity, temperature, and surface temperature profiles are shown both graphically and in tabular forms for the different values of the parameters correlated with the problem.