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Conditional Lie Backlund Symmetries of hamilton-jacobi equations

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Chinese Physics Letters 2007年第12期24卷 3293-3296页

作者：王丽真勾明屈长征 Center for Nonlinear Studies Northwest University Xi'an 710069 Department of Mathematics Northwest University Xi'an 710069

The conditional Lie Bgcklund symmetry method, as a generalization of the conditional symmetry and Lie Bgcklund symmetry methods, is developed to study the hamilton-jacobi equations. It is shown that the equation ut = ux^n＋1 4- B（u）ux 4- C（u） admits a class of conditional Lie Bgcklund symmetry for certain functions B（u） and C（u）. As a result, a complete description of structure of solutions to the resulting equations associated to the conditional Lie Backlund symmetry is performed.

关键词： Conditional Lie Backlund Symmetries hamilton-jacobi equations

THE LARGE TIME GENERIC FORM OF THE SOLUTION TO hamilton-jacobi equations

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Acta Mathematica Scientia 2011年第6期31卷 2265-2277页

作者：王靖华温海瑞赵引川 Academy of Mathematics and System Sciences The Chinese Academy of Sciences Department of Mathematics Beijing Institute of Technology Department of Mathematics and Physics North China Electric Power University

We use Hopf-Lax formula to study local regularity of solution to hamilton- jacobi （HJ） equations of multi-dimensional space variables with convex hamiltonian. Then we give the large time generic form of the solution to HJ equation, i.e. for most initial data there exists a constant T 〉 0, which depends only on the hamiltonian and initial datum, for t 〉 T the solution of the IVP （1.1） is smooth except for ~ smooth n-dimensional hypersurface, across which Du（x, t） is discontinuous. And we show that the hypersurface 1 tends asymptotically to a given hypersurface with rate t-1/4.

关键词： HopfoLax formula hamilton-jacobi equations local regularity large time generic form

Exponential Convergence to Time-Periodic Viscosity Solutions in Time-Periodic hamilton-jacobi equations

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Chinese Annals of Mathematics,Series B 2018年第1期39卷 69-82页

作者： Kaizhi WANG School of Mathematical Sciences Shanghai Jiao Tong University

Consider the Cauchy problem of a time-periodic hamilton-jacobi equation on a closed manifold,where the hamiltonian satisfies the condition:The Aubry set of the corresponding hamiltonian system consists of one hyperbolic 1-periodic *** is proved that the unique viscosity solution of Cauchy problem converges exponentially fast to a1-periodic viscosity solution of the hamilton-jacobi equation as the time tends to infinity.

关键词： hamilton-jacobi equations Viscosity solutions Weak KAM theory

CONVERGENCE OF FINITE VOLUME SCHEMES FOR hamilton-jacobi equations WITH DIRICHLET BOUNDARY CONDITIONS

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Journal of Computational Mathematics 2015年第3期33卷 227-247页

作者： Kwangil Kim Yonghai Li School of Mathematics Jilin University Changchun 130012 China Department of Mathematics University of Science Pyongyang DPR Korea

We study numerical methods for time-dependent hamilton-jacobi equations with weak Dirichlet boundary conditions. We first propose a new class of abstract monotone approximation schemes and get a convergence rate of 1/2 . Then, according to the abstract convergence results, by newly constructing monotone finite volume approximations on interior and boundary points, we obtain convergent finite volume schemes for time-dependent hamilton-jacobi equations with weak Dirichlet boundary conditions. Finally give some numerical results.

关键词： hamilton-jacobi equations Dirichlet boundary conditions Finite volume Monotone schemes.

Arc Length-Based WENO Scheme for hamilton-jacobi equations

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Communications on Applied Mathematics and Computation 2021年第3期3卷 481-496页

作者： Rathan Samala Biswarup Biswas Faculty of Mathematics Department of Humanities and SciencesIndian Institute of Petroleum and Energy-VisakhapatnamVisakhapatnam 530003India Department of Mathematics Indian Institute of Technology-DelhiNew Delhi 110016India

In this article,novel smoothness indicators are presented for calculating the nonlinear weights of the weighted essentially non-oscillatory scheme to approximate the viscosity numerical solutions of hamilton-jacobi *** novel smoothness indicators are constructed from the derivatives of reconstructed polynomials over each *** constructed smoothness indicators measure the arc-length of the reconstructed polynomials so that the new nonlinear weights could get less absolute truncation error and give a high-resolution numerical *** numerical tests are conducted and presented to show the performance capability and the numerical accuracy of the proposed scheme with the comparison to the classical WENO scheme.

关键词： Finite difference hamilton-jacobi equations WENO scheme Length of the curve Smoothness indicators Nonlinear weights

DISCONTINUOUS SOLUTIONS IN L~∞ FOR hamilton-jacobi equations

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Chinese Annals of Mathematics,Series B 2000年第2期21卷 165-186页

作者： CHENGUIQIANG SUBo ：DepartmentofMathematics NorthwesternUniversity2033SheridanRoadEvanstonIL60208-2730USA DepartmentofMathematics UniversityofWisconsinatMadisonMadisonWI53706-1380USA.

An approach is introduced to construct global discontinuous solutions in L~∞ for hamiltonjacobi equations. This approach allows the initial data only in L~∞ and applies to the equations with nonconvex hamiltonians. The profit functions are introduced to formulate the notion of discoatinuous solutions in L~∞. The existence of global discontinuous solutions in L~∞ is established. These solutions in L~∞ coincide with the viscosity solutions and the minimax solutions, provided that the initial data are continuous. A prototypical equation is analyzed to examine the L~∞ stability of our L~∞ solutions. The analysis also shows that global discontinuous solutions are determined by the topology in which the initial data are approximated.

关键词： hamilton-jacobi equations Discontinuous solutions Profit functions Viscosity solutions Madman solutions Stability

Dual‑Wind Discontinuous Galerkin Methods for Stationary hamilton‑jacobi equations and Regularized hamilton‑jacobi equations

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Communications on Applied Mathematics and Computation 2022年第2期4卷 563-596页

作者： Xiaobing Feng Thomas Lewis Aaron Rapp Department of Mathematics The University of TennesseeKnoxvilleTN 37996USA Department of Mathematics and Statistics The University of North Carolina at GreensboroGreensboroNC 27402USA Department of Mathematical Sciences University of the Virgin IslandsKingshillUSVI 00850-9781US Virgin Islands

This paper develops and analyzes a new family of dual-wind discontinuous Galerkin(DG)methods for stationary hamilton-jacobi equations and their vanishing viscosity *** new DG methods are designed using the DG fnite element discrete calculus framework of[17]that defnes discrete diferential operators to replace continuous differential operators when discretizing a partial diferential equation(PDE).The proposed methods,which are non-monotone,utilize a dual-winding methodology and a new skewsymmetric DG derivative operator that,when combined,eliminate the need for choosing indeterminable penalty *** relationship between these new methods and the local DG methods proposed in[38]for hamilton-jacobi equations as well as the generalized-monotone fnite diference methods proposed in[13]and corresponding DG methods proposed in[12]for fully nonlinear second order PDEs is also *** and stability are established for the proposed dual-wind DG *** stability results are shown to hold independent of the scaling of the stabilizer allowing for choices that go beyond the Godunov barrier for monotone *** experiments are provided to gauge the performance of the new methods.

关键词： hamilton-jacobi equations Discontinuous Galerkin methods Vanishing viscosity method

Aubry-Mather theory for contact hamiltonian systems Ⅲ

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Science China Mathematics 2024年第11期67卷 2541-2570页

作者： Panrui Ni Lin Wang Shanghai Center for Mathematical Sciences Fudan UniversityShanghai 200433China School of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

By exploiting the contact hamiltonian dynamics(T*M×R,Φ_(t))around the Aubry set of contact hamiltonian systems,we provide a relation among the Mather set,theΦ_(t)-recurrent set,the strongly static set,the Aubry set,the Ma?éset,and theΦ_(t)-non-wandering ***,we consider the strongly static set,as a new flow-invariant set between the Mather set and the Aubry set in the strictly increasing *** show that this set plays an essential role in the representation of certain minimal forward weak Kolmogorov-Arnold-Moser(KAM)solutions and the existence of transitive orbits around the Aubry set.

关键词： Aubry-Mather theory weak KAM theory contact hamiltonian systems hamilton-jacobi equations

A New Method to Study Hawking Radiation of Charged Particle from Stationary Axisymmetric Sen Black Hole

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Chinese Physics Letters 2007年第1期24卷 39-41页

作者：杨树政陈德友 Institute of Theoretical Physics China West Normal University Nanchong 637002

Taking the self-gravitation interaction and energy conservation,charge conservation and angular momentum conservation into accpunt, we discuss the tunnelling characteristics of the charged particle from Sen black hole by the hamilton-jacobi method. The result shows that the tunnelling probability is related to the change of Bekenstein-Hawking entropy, and the actual radiation spectrum deviates from the pure thermal one, which is consistent with the result of Parikh and Wilczek and gives a new method to correct the Hawking pure thermal spectrum of Sen black hole.

关键词： ENERGY conservation ANGULAR momentum (Nuclear physics) PARTICLES hamilton-jacobi equations