Radially symmetric solutions of a non-linear problem with Neumann boundary condition in one dimension like self similar solutions via finite differences

2018 ◽  
Vol 11 (48) ◽  
pp. 2349-2356
Author(s):  
A. M. Marin ◽  
R. D. Ortiz ◽  
Alfredo-Yerman Cortes-Verbel
Keyword(s):  
Boundary Condition ◽  
Finite Differences ◽  
Neumann Boundary Condition ◽  
Linear Problem ◽  
Neumann Boundary ◽  
One Dimension ◽  
Non Linear ◽  
Self Similar ◽  
Radially Symmetric Solutions ◽  
Similar Solutions

scholarly journals Prescribing Gaussian and Geodesic Curvature on Disks

2018 ◽  
Vol 18 (3) ◽  
pp. 453-468 ◽  
Author(s):  
Sergio Cruz-Blázquez ◽  
David Ruiz
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Type Equation ◽  
Neumann Boundary ◽  
Geodesic Curvature ◽  
Liouville Type ◽  
Conformal Change ◽  
Variational Framework ◽  
Non Linear

Abstract In this paper, we consider the problem of prescribing the Gaussian and geodesic curvature on a disk and its boundary, respectively, via a conformal change of the metric. This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be completely new in the literature. We are able to find minimizers under symmetry assumptions.

Inverse spectral problem of an anharmonic oscillator on a half-axis with the Neumann boundary condition

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Agil K. Khanmamedov ◽  
Nigar F. Gafarova
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Inverse Spectral Problem ◽  
Anharmonic Oscillator ◽  
Neumann Boundary ◽  
Effective Algorithm ◽  
Inverse Spectral Problems ◽  
Main Equation ◽  
Inverse Spectral ◽  
Half Axis

AbstractAn anharmonic oscillator {T(q)=-\frac{d^{2}}{dx^{2}}+x^{2}+q(x)} on the half-axis {0\leq x<\infty} with the Neumann boundary condition is considered. By means of transformation operators, the direct and inverse spectral problems are studied. We obtain the main integral equations of the inverse problem and prove that the main equation is uniquely solvable. An effective algorithm for reconstruction of perturbed potential is indicated.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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