A singularly perturbed reaction diffusion problem forthe nonlinear boundary condition with two parameters

A class of singularly perturbed initial boundary valueproblems of reaction diffusion equations for the nonlinear boundarycondition with two parameters is considered. Under suitableconditions, by using the theory of differential inequalities, theexistence and the asymptotic behaviour of the solution for the initial boundaryvalue problem are studied. The obtained solution indicates thatthere are initial and boundary layers and the thickness of theboundary layer is less than the thickness of the initial layer.