Nonlinear stability of a diffusion equation

Similarity Reductions for a Nonlinear Diffusion Equation

Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as...

Exponential Stability in a Nonlinear String Equation

We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

Stability Analysis of Scalar Advection-Diffusion Equation

This note recounts detailed stability and accuracy analysis of a scalar advection-diffusion equation.

Hyers-Ulam Stability of Nonlinear Integral Equation

Nonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis

The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensio...