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Conservation law of harmonic mappings in supercritical dimensions
Published 2024-09-01“…As an application, we obtain a conservation law for weakly harmonic mappings around regular points in supercritical dimensions.…”
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The shallow water equations: conservation laws and symplectic geometry
Published 1987-01-01“…By using the hodograph method we construct solutions, conservation laws, and Böcklund transformations for these equations. …”
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Best practice mechanisms for biodiversity conservation law and policy
Published 2023-01-01“…We reviewed 128 publications from around the world to ascertain and synthesise best practices in law and policy that aim to protect and conserve biodiversity (herein termed ‘biodiversity conservation law’). The literature demonstrated that when it comes to biodiversity conservation law, the concept of ‘best practice’ is elusive, and does not necessarily equate to a reversal in species decline. …”
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Analysis of the Symmetries and Conservation Laws of the Nonlinear Jaulent-Miodek Equation
Published 2014-01-01“…The Lie invariants associated with the symmetry generators as well as the corresponding similarity reduced equations are also pointed out. And conservation laws of the J-M equation are presented with two steps: firstly, finding multipliers for computation of conservation laws and, secondly, symbolic computation of conservation laws will be applied.…”
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Invariant Solutions and Conservation Laws of the Time-Fractional Telegraph Equation
Published 2023-01-01“…The similarity reduction and conservation laws to the fractional telegraph equation are found.…”
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Error estimates for scalar conservation laws by a kinetic approach
Published 2006-01-01“…We use the kinetic approach of Perthame and Tadmor (1991) to calculate the error estimates for general scalar conservation laws governing problems in gas dynamics or fluid mechanics in general. …”
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On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations
Published 2017-01-01“…Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases.…”
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Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws
Published 2009-01-01“…We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. …”
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On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation
Published 2013-01-01“…In addition, we also derive the conservation laws for the coupled Kadomtsev-Petviashvili equation.…”
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Symmetry, Pulson Solution, and Conservation Laws of the Holm-Hone Equation
Published 2019-01-01“…We mainly study its symmetry properties, travelling wave solutions, and conservation laws. The symmetry group and its one-dimensional optimal system are given. …”
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Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation
Published 2013-01-01“…Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1)-dimensional Boussinesq equation.…”
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On the Conservation Laws and Exact Solutions of a Modified Hunter-Saxton Equation
Published 2014-01-01“…We obtain local conservation laws using the nonlocal conservation method and multiplier approach. …”
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On optimal regularity estimates for finite-entropy solutions of scalar conservation laws
Published 2023-03-01“…We consider finite-entropy solutions of scalar conservation laws $u_t +a(u)_x =0$, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. …”
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High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws
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Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions
Published 2013-01-01“…We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. …”
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On the Definition of Energy for a Continuum, Its Conservation Laws, and the Energy-Momentum Tensor
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Nonlinear asymptotic stability in $L^\infty $ for Lipschitz solutions to scalar conservation laws
Published 2024-07-01“…In this note, we show nonlinear stability in $L^\infty $ for Lipschitz solutions to genuinely nonlinear, multi-dimensional scalar conservation laws. As an application, we are able to compute algebraic decay rates of the $L^\infty $ norm of perturbations of global-in-time Lipschitz solutions, including perturbations of planar rarefaction waves. …”
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Approximate Symmetry Analysis and Approximate Conservation Laws of Perturbed KdV Equation
Published 2018-01-01“…The approximate invariants of the presented approximate symmetries and some new approximately invariant solutions to the equation are constructed. Moreover, the conservation laws have been constructed by using partial Lagrangian method.…”
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Optimized Weighted Essentially Nonoscillatory Third-Order Schemes for Hyperbolic Conservation Laws
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