Results 251 to 260 of about 4,288,813 (291)

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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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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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 \((0,1)\)
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A nonlinear thermoelastic system with nonlinear boundary conditions

Journal of Evolution Equations, 2015
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Clark, H. R., Clark, M. R., Louredo, A. T., Oliveira, A. M.   +3 more
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A nonlinear boundary value problem containing nonstandard boundary conditions

Applied Mathematics and Computation, 2002
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Marián Slodicka, Hennie De Schepper
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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.
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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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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.
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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
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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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