Results 251 to 260 of about 9,215,429 (289)

On a Nonlocal BVP with Nonlinear Boundary Conditions

Results in Mathematics, 2012
The author considers the existence of a positive solution to a boundary value problem where one of the boundary conditions is allowed to be nonlocal and nonlinear, namely \[ \begin{gathered} u''(t)+f(t,u(t))=0,\;t \in (0,1),\\ u(0) =H_{1}(\varphi (u))+\int_E H_{2}(s,u(s))\,ds,\;u(1) =0.\\ \end{gathered} \] Here, \(E\) is a measurable subset of \((0,1)\)
openaire   +1 more source

A nonlinear thermoelastic system with nonlinear boundary conditions

Journal of Evolution Equations, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Clark, H. R., Clark, M. R., Louredo, A. T., Oliveira, A. M.   +3 more
openaire   +1 more source

A nonlinear boundary value problem containing nonstandard boundary conditions

Applied Mathematics and Computation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marián Slodicka, Hennie De Schepper
openaire   +2 more sources

Nonlinear Boundary Conditions

2014
In this chapter we will study reaction-diffusion equations with nonlinear boundary conditions. Problems of this type can arise in various chemical and biological applications. We will begin with one-dimensional problems in bounded intervals. After that we will study travelling waves in two-dimensional strips.
openaire   +1 more source

Nonlinear Artificial Boundary Conditions

2013
In this chapter, we discuss the nonlinear ABCs for Burgers equation, Kardar-Parisi-Zhang equation, and Schrodinger equation on unbounded domains. By using artificial boundaries, the original problems are reduced to initial boundary value problems on bounded computational domains.
Houde Han, Xiaonan Wu
openaire   +1 more source

SOME QUALITATIVE DYNAMICS OF NONLINEAR BOUNDARY CONDITIONS

International Journal of Bifurcation and Chaos, 2002
In this paper we survey some recent results on the behavior of solutions of parabolic equations subjected to nonlinear boundary conditions. The results range from local existence and regularity of solutions, to global existence, dissipativeness and existence of attractors, and to blow-up in finite time.
openaire   +2 more sources

Study of an elliptic problem with nonlinear boundary conditions

Mathematical Methods in the Applied Sciences, 1987
AbstractWe consider the problem of finding on a trapezium a harmonic function u the normal derivative of which is equal on one side to λ exp(u). We prove the existence of a solution branch (λ,u(λ)) with a turning point and, for the case of the square, the presence of bifurcations. The “inverse power” algorithm converges on a part of the branch.
Ph. Caussignac, J. Descloux, J. Rappaz, J. Rappaz, J. C. Nedelec   +4 more
openaire   +2 more sources

Absorbing boundary conditions for nonlinear Schrödinger equations

Physical Review E, 2006
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 ...
Zhenli, Xu, Houde, Han
openaire   +2 more sources

Systems with Nonlinear Boundary Conditions

1992
This chapter gives a treatment for coupled system of equations with nonlinear boundary conditions analogous to that for coupled systems with linear boundary conditions. The system under consideration can be coupled through the boundary conditions or through the differential equations. For systems of two equations coupled through the boundary conditions,
openaire   +1 more source

Evolution Problems with Nonlinear Nonlocal Boundary Conditions

Journal of Dynamics and Differential Equations, 2013
The authors consider a nonlinear evolution problem with nonlinear nonlocal boundary conditions. They concentrate on existence results obtained by applying the degree theory for function triples with a Fredholm function developed in [the third author, Topological analysis. From the basics to the triple degree for nonlinear Fredholm inclusions.
BENEDETTI, Irene, Valentina Taddei, Martin Väth   +2 more
openaire   +3 more sources