New blow‐up conditions to p ‐Laplace type nonlinear parabolic equations under nonlinear boundary conditions

A Remark on the Blowup of Solutions to the Laplace Equations with Nonlinear Dynamical Boundary Conditions

Blow-up in the Parabolic Problems under Nonlinear Boundary Conditions

In this paper, I consider nonlinear parabolic problems under nonlinear boundary conditions. I establish respectively the conditions on nonlinearities to guarantee that ( , ) u x t exists globally or blows up at some finite time. If blow-up occurs, an upper bound for the blow-up time is derived, under somewhat more restrictive conditions, lower bounds for the blow-up time are also derived.

Nonlinear Boundary Conditions for Elliptic Equations

This work is devoted to the study of the elliptic equation ∆u = f(x, u) in a bounded domain Ω ⊂ Rn with a nonlinear boundary condition. We obtain various existence results applying coincidence degree theory and the method of upper and lower solutions.

Absorbing boundary conditions for nonlinear Schrödinger equations.

A local time-splitting method (LTSM) is developed to design absorbing boundary conditions for numerical solutions of time-dependent nonlinear Schrödinger equations associated with open boundaries. These boundary conditions are significant for numerical simulations of propagations of nonlinear waves in physical applications, such as nonlinear fiber optics and Bose-Einstein condensations. Numeric...

Ordinary Differential Equations with Nonlinear Boundary Conditions

The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems. 2000 Mathematics Subject Classification: 34A45, 34B15, 34A40.