Results 321 to 330 of about 1,226,678 (360)

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.
V. Volpert
semanticscholar   +2 more sources

On Nonlinear Boundary Conditions Involving Decomposable Linear Functionals

Proceedings of the Edinburgh Mathematical Society, 2014
AbstractIn this paper we consider the existence of a positive solution to boundary-value problems with non-local nonlinear boundary conditions, the archetypical example being −y″(t) = λf(t,y(t)),t∈ (0, 1),y(0) =H(φ(y)),y(1) = 0. Here,His a nonlinear function,λ> 0 is a parameter andφis a linear functional that is realized as a Lebesgue—Stieltjes ...
C. Goodrich
semanticscholar   +3 more sources

Boundary-value problems with nonlinear boundary conditions

Nonlinearity, 1988
The authors deal with a general boundary value problem of the type: \(x'=F(t,x),T(x)=y,y\in R^ n\) where \(F(t,x)=A(t)x+f(t,x)\) and T is a continuous but not necessarily linear operator. It is shown that under suitable conditions the problem has at least one solution. The proof relies on a fixed-point theorem for condensing maps.
ANICHINI, GIUSEPPE, CONTI, GIUSEPPE
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Reconstructing unknown nonlinear boundary conditions in a time‐fractional inverse reaction–diffusion–convection problem

Numerical Methods for Partial Differential Equations, 2018
This paper has focused on unknown functions identification in nonlinear boundary conditions of an inverse problem of a time‐fractional reaction–diffusion–convection equation. This inverse problem is generally ill‐posed in the sense of stability, that is,
A. Babaei, S. Banihashemi
semanticscholar   +1 more source

Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

Acta Mathematica Sinica, English Series, 2005
The authors study the existence and nonexistence of global positive solutions to the following nonlinear parabolic equation with nonlinear boundary conditions \[ \begin{aligned} & (u^k)_t = \Delta_mu,\quad x \in\Omega, \quad t > 0,\\ & \nabla_m u\cdot\nu = u^{\alpha},\quad x\in \partial\Omega, \quad t > 0,\\ & u(x,0) = u_0(x),\quad x\in\bar\Omega, \end{
Sun, Wenjun, Wang, Shu
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A nonlinear boundary value problem containing nonstandard boundary conditions

Applied Mathematics and Computation, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Slodička, M., De Schepper, H.
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
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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.
Irene Benedetti, TADDEI, Valentina, Martin Vath   +2 more
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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
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Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

Journal of Differential Equations, 2018
In this paper, we consider a domain Ω e ⊂ R N , N ≥ 2 , with a very rough boundary depending on e. For instance, if N = 3 Ω e has the form of a brush with an e-periodic distribution of thin cylindrical teeth with fixed height and a small diameter of ...
A. Gaudiello, T. Mel'nyk
semanticscholar   +1 more source