Life span for solutions of the heat equation with a nonlinear boundary condition

Life Span for Solutions of the Heat Equation with a Nonlinear Boundary Condition

In this note we obtain estimates in terms of the size of the initial data for the blow-up time of positive solutions of the heat equation in R+ with a nonlinear boundary condition −ux(0, t) = up(0, t). Introduction. In this note we obtain estimates for the blow-up time of positive solutions of the following parabolic problem (1)  ut = uxx in R+ × (0, Tλ), −ux(0, t) = u(0, t) in (0, Tλ), u(x, ...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Fréchet Differentiability of the Solution of the Heat Equation With Respect to a Nonlinear Boundary Condition

Fr echet diierentiability of the solution of the heat equation with respect to a nonlinear boundary condition Arnd RR osch Abstract. Consider the heat equation with a nonlinear function in the boundary condition which depends only on the boundary values x of the solution u of the initial-boundary value problem. The function belongs to a set of admissible diierentiable or uniformly Lipschitz con...