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A Nonlinear Scheme Preserving Maximum Principle for Heterogeneous Anisotropic Diffusion Equation
Journal of Computational and Applied MathematicsThe authors present an improved finite volume method preserving the discrete maximum principle for the diffusion problem with heterogeneous coefficient. This scheme can deal with various cases, including that arbitrary cell edges are the discontinuous line, and then overcomes the defect of the existing schemes which assume that there has only one ...
Guangwei Yuan, Zhiqiang Sheng
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Nonlinear Maximum Principles for Dissipative Linear Nonlocal Operators and Applications
Geometric and Functional Analysis, 2012 We obtain a family of nonlinear maximum principles for linear dissipa- tive nonlocal operators, that are general, robust, and versatile. We use these nonlinear bounds to provide transparent proofs of global regularity for critical SQG and critical d ...
Peter Constantin, Vlad Vicol
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A nonlinear version of the Kantorovich–Rubinstein maximum principle
Nonlinear Analysis: Theory, Methods & Applications, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gacki, Henryk, Lasota, Andrzej
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Maximum-entropy principle for nonlinear hydrodynamic transport in semiconductors
Continuum Mechanics and Thermodynamics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
TROVATO, Massimo, FALSAPERLA, PAOLO
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The Maximum Principle and Controllability of Nonlinear Equations
SIAM Journal on Control, 1972The main result proved is that a nonlinear control equation is controllable if a related linear equation is controllable. The result allows the set of control values to be discrete and it is not assumed that “small” values of the control are available. The methods used are closely related to the Pontryagin maximum principle.
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Maximum Principle for Nonlinear Parabolic Equations
Journal of Mathematical Sciences, 2018In this paper, the author gives some maximum principles for solutions of some nonlinear parabolic equations. The author considers first, the parabolic equation \[ \mathcal{L}u-u_{t}=f(x,t,u,Du),\text{ in }\Omega\cup\gamma\Omega\tag{1} \] where {\parindent=6mm \begin{itemize}\item[{\(\bullet\)}] \(\Omega\subset\mathbb{R}^n\times(0,\infty)\) is an ...
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Maximum entropy principle and nonlinear stochastic oscillators
Physica A: Statistical Mechanics and its Applications, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sobczyk, K., Trȩbicki, J.
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ON THE MAXIMUM PRINCIPLE FOR NONLINEAR PARABOLIC AND ELLIPTIC EQUATIONS
Mathematics of the USSR-Izvestiya, 1979A maximum principle in Sobolev spaces is proved for nonlinear elliptic and parabolic equations. The proof is based on estimates for the maximum of the solutions of a parabolic equation with measurable coefficients, in terms of the norm of the right side. The results of the paper are analogous to results of A. D.
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Maximum Principle of a Class of Nonlinear PDE Systems
1989 American Control Conference, 1989In Banach spaces with either L2 or L? type norm a generalized integral version of Maximum Principle for a class of nonlinear PDEs and a general cost functional is derived. The developed theory is applied to the design of a two-dimensional nonlinear hyperbolic system.
G. Huang, T.S. Tang
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A Nonlinear Finite Volume Scheme Preserving Maximum Principle for Diffusion Equations
Communications in Computational Physics, 2021In this paper we propose a new nonlinear cell-centered finite volume scheme on general polygonal meshes for two dimensional anisotropic diffusion problems, which preserves discrete maximum principle (DMP). The scheme is based on the so-called diamond scheme with a nonlinear treatment on its tangential flux to obtain a local maximum principle (LMP ...
Xu, Jinjing +3 more
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