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Acta Mathematicae Applicatae Sinica 1997年第2期13卷 235-242页

作者：詹毅 Department of Applied Mathematics Tsinghua University Beijing China

In [1] we construct a unique bounded H■lder continuous viscosity solution for the nonlinear PDEs with the evolution p-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however,this result does not include the anisotropic case.

关键词： Degenerate p-Laplacian anisotropic viscosity solution finite propagation positivity H■lder continuity Lipschitz continuity free boundary,asymptotic spherical symmetricity

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Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations

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Science China Mathematics 2021年第8期64卷 1789-1800页

作者： Cui Chen Ya-Nan Wang Jun Yan The Faculty of Science Jiangsu UniversityZhenjiang 212013China School of Mathematical Sciences Nanjing Normal UniversityNanjing 210097China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematics Shanghai 200433China

In this paper,we investigate the non-autonomous Hamilton-Jacobi equation{ə_(t)u+H(t,x,ə_(x)=0,u(x,t)_(0))=φ(x),x∈M where H is 1-periodic with respect to t and M is a compact Riemannian manifold without *** obtain the viscosity solution denoted by T_(t_(0))^(t)φ(x)and show T_(t_(0))^(t)φ(x)converges uniformly to a time-periodic viscosity solution u^(*)(x,t)ofə_(t)u+H(t,x,ə_(x)u,u)=0.

关键词： Hamilton-Jacobi equation viscosity solution large-time behavior

A viscosity solution Approach to Valuation of Passport Options in A Jump-Diffusion Model

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A Viscosity Solution Approach to Valuation of Passport Optio...

viscosity solutionS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

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作者： Bian Baojun,Wang Yang Department of Mathematics,Tongji University,Shanghai 200092,P.R.China

We consider the pricing problem of European passport option when underlying asset follows a jump-diffusion *** derive the pricing equation and establish the comparison principle,uniqueness result and convexity preserv... 详细信息

关键词： Passport option Jump-diffusion viscosity solution Uniqueness Convexity preserving

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Acta Mathematica Scientia 2010年第1期30卷 187-202页

作者：边保军王杨张寄洲 Department of Mathematics Tongji University Mathematics and Science College Shanghai Normal University

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.

关键词： passport option HJB equation viscosity solution uniqueness convexitypreserving

viscosity solutions of Monotonic Functional Parabolic PDE

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Acta Mathematica Sinica,English Series 2004年第4期20卷 739-748页

作者： WeiAnLIU GangLU SchoolofMathematicsandStatistics WuhanUniversityWuhan430072P.R.China DepartmentofMathematics CentralChinaNormalUniversityWuhan430079P.R.China

In this paper,by the technique of coupled solutions,the notion of viscosity solution is ex- tended to quasi-monotonic fully nonlinear parabolic equations with delay,which involves many models arising from optimal control theory,economy and finance,biology *** comparison,existence and uniqueness are *** the results are applied to the retarded Bellman equations.

关键词： viscosity solution Functional PDE Technique of coupled solutions Retarded Belhnan equations

viscosity solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian

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Acta Mathematica Sinica,English Series 2015年第2期31卷 255-271页

作者： Fang LIU Xiao Ping YANG Department of Applied Mathematics School of Science Nanjing University of Science & Technology

We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, wher... 详细信息

关键词： Parabolic equation infinity Laplacian viscosity solution inhomogeneous equation comparison principle existence

viscosity solutions of Monotonic Functional Parabolic PDE

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Acta Mathematicae Applicatae Sinica 2004年第4期 739-748页

作者： Wei An LIU School of Mathematics and Statistics,Wuhan University,Wuhan 430072,P.R.China Gang LU Department of Mathematics,Central China Normal University,Wuhan 430079,P.R.China

In this paper,by the technique of coupled solutions,the notion of viscosity solution is ex-tended to quasi-monotonic fully nonlinear parabolic equations with delay,which involves many modelsarising from optimal control theory,economy and finance,biology *** comparison,existence anduniqueness are *** the results are applied to the retarded Bellman equations.

关键词： viscosity solution Functional PDE Technique of coupled solutions Retarded Bellman equations

Existence and Uniqueness of viscosity solutions for Nonlinear Variational Inequalities Associated with Mixed Control

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Chinese Annals of Mathematics,Series B 2020年第5期41卷 793-820页

作者： Shipei HU Department of Mathematics Jiaxing UniversityJiaxing 314001ZhejiangChina

The author investigates the nonlinear parabolic variational inequality derived from the mixed stochastic control problem on finite *** that some suffi-ciently smooth conditions hold,by the dynamic programming principle,the author builds the Hamilton-Jacobi-Bellman(HJB for short)variational inequality for the value *** author also proves that the value function is the unique viscosity solution of the HJB variational inequality and gives an application to the quasi-variational inequality.

关键词： Optimal stopping Mixed control Variational inequality viscosity solution

viscosity solutionS DEFINED BY RIGHT DIFFERENTIALS

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Journal of Systems Science & Complexity 2002年第2期15卷 146-154页

作者： Lou Hongwei Mathematical Department Fudan University 上海 200433

Abstract. It is proved that for some partial differential equations, the classical notion ofviscosity solution can be defined via right-subdifferentials and superdifferentials of contin-uous functions.

关键词： viscosity solution subdifferential superdifferential right-differential.

THE BERNSTEIN ESTIMATES OF viscosity solutionS OF LINEAR PARABOLIC EQUATIONS

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Acta Mathematicae Applicatae Sinica 1995年第3期11卷 255-262页

作者：詹毅 Department of Applied Mathematics Tsinghua University Beijing China

This paper is concerned with the Bernstein estimates of viscosity solutions of the Cauchy problems for linear parabolic equations. The techniques of viscosity solution method given by *** and P.L. Lions in [1] allow us to deduce the estimates without differentiating the equation,which is in a way completely different from the classical one. We mainly get the estimate of under the corresponding assumptions on the smoothness of solutions and the known functions in the equation.

关键词： Bernstein estimates viscosity solution linear parabolic equations