Homogenization of elliptic systems with Neumann boundary conditions

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.

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

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2019-0074 ◽

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}.

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Critique on “Volume penalization for inhomogeneous Neumann boundary conditions modeling scalar flux in complicated geometry”

Journal of Computational Physics ◽

10.1016/j.jcp.2021.110163 ◽

2021 ◽

Vol 433 ◽

pp. 110163

Author(s):

Ramakrishnan Thirumalaisamy ◽

Nishant Nangia ◽

Amneet Pal Singh Bhalla

Keyword(s):

Boundary Conditions ◽

Neumann Boundary ◽

Neumann Boundary Conditions ◽

Scalar Flux ◽

Complicated Geometry

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

Symmetry ◽

10.3390/sym11040469 ◽

2019 ◽

Vol 11 (4) ◽

pp. 469 ◽

Cited By ~ 2

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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