scholarly journals Weak solutions to hyperbolic problems with inhomogeneous Dirichlet and Neumann boundary conditions

2013 ◽  
Vol 37 (5) ◽  
pp. 2623-2629 ◽  
Author(s):  
Sıdıka Şule Şener ◽  
Yeşim Saraç ◽  
Murat Subaşı
Keyword(s):  
Boundary Conditions ◽  
Weak Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Hyperbolic Problems

scholarly journals Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Ghasem A. Afrouzi ◽  
Z. Naghizadeh ◽  
Nguyen Thanh Chung
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Nonlocal Problems ◽  
Mapping Theory ◽  
Nonlinear Neumann Boundary Conditions

In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.

scholarly journals Extremal solutions to Liouville–Gelfand type elliptic problems with nonlinear Neumann boundary conditions

2015 ◽  
Vol 17 (03) ◽  
pp. 1450016
Author(s):  
Futoshi Takahashi
Keyword(s):  
Boundary Conditions ◽  
Weak Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Extremal Solutions ◽  
Smooth Bounded Domain ◽  
Suitable Notion ◽  
Extremal Parameter ◽  
Nonlinear Neumann Boundary Conditions ◽  
Increasing Function

Consider the Liouville–Gelfand type problems with nonlinear Neumann boundary conditions [Formula: see text] where Ω ⊂ ℝN, N ≥ 2, is a smooth bounded domain, f : [0, +∞) → (0, +∞) is a smooth, strictly positive, convex, increasing function with superlinear at +∞, and λ > 0 is a parameter. In this paper, after introducing a suitable notion of weak solutions, we prove several properties of extremal solutions u* corresponding to λ = λ*, called an extremal parameter, such as regularity, uniqueness, and the existence of weak eigenfunctions associated to the linearized extremal problem.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Recovering differential operators with two constant delays under Dirichlet/Neumann boundary conditions

2020 ◽  
Vol 28 (2) ◽  
pp. 237-241
Author(s):  
Biljana M. Vojvodic ◽  
Vladimir M. Vladicic
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

AbstractThis paper deals with non-self-adjoint differential operators with two constant delays generated by {-y^{\prime\prime}+q_{1}(x)y(x-\tau_{1})+(-1)^{i}q_{2}(x)y(x-\tau_{2})}, where {\frac{\pi}{3}\leq\tau_{2}<\frac{\pi}{2}<2\tau_{2}\leq\tau_{1}<\pi} and potentials {q_{j}} are real-valued functions, {q_{j}\in L^{2}[0,\pi]}. We will prove that the delays and the potentials are uniquely determined from the spectra of four boundary value problems: two of them under boundary conditions {y(0)=y(\pi)=0} and the remaining two under boundary conditions {y(0)=y^{\prime}(\pi)=0}.

scholarly journals Numerical Solution of Nonlinear Schrödinger Equation with Neumann Boundary Conditions Using Quintic B-Spline Galerkin Method

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 469 ◽  
Author(s):  
Azhar Iqbal ◽  
Nur Nadiah Abd Hamid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spline Method ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
B Spline

This paper is concerned with the numerical solution of the nonlinear Schrödinger (NLS) equation with Neumann boundary conditions by quintic B-spline Galerkin finite element method as the shape and weight functions over the finite domain. The Galerkin B-spline method is more efficient and simpler than the general Galerkin finite element method. For the Galerkin B-spline method, the Crank Nicolson and finite difference schemes are applied for nodal parameters and for time integration. Two numerical problems are discussed to demonstrate the accuracy and feasibility of the proposed method. The error norms L 2 , L ∞ and conservation laws I 1 ,   I 2 are calculated to check the accuracy and feasibility of the method. The results of the scheme are compared with previously obtained approximate solutions and are found to be in good agreement.

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