Singular limit and exact decay rate of a nonlinear elliptic equation

On a singular nonlinear semilinear elliptic problem

where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under variou...

Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{beta}(t-s)^{-alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable is first introduced in order to obtain a new equation with smoother solution‎. ‎Error analysis of this method is also ...

Exact and numerical solutions for nonlinear differential equation of Jeffrey-Hamel flow

Attractors for the Nonlinear Elliptic Boundary Value Problems and Their Parabolic Singular Limit

We apply the dynamical approach to the study of the second order semilinear elliptic boundary value problem in a cylindrical domain with a small parameter ε at the second derivative with respect to the variable t corresponding to the axis of the cylinder. We prove that, under natural assumptions on the nonlinear interaction function f and the external forces g(t), this problem possesses the uni...

A Singular Nonlinear Volterra Integral Equation

This paper concerns the integral equation