This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admi...This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.展开更多
Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechan...Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, it is proved there exists at least one solution.展开更多
In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear dif...The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).展开更多
In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up...In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. (Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55(2006), 1113-1134). Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.展开更多
We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boun...We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximM monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.展开更多
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove ...We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.展开更多
Iterative techniques for solving optimal control systems governed by parabolic varia-tional inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equatio...Iterative techniques for solving optimal control systems governed by parabolic varia-tional inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equations and nonlinear conjugate gradient methods to solve the discrete optimal control problem. Convergence results and numerical experiments are presented.展开更多
We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-si...We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-sided estimates for the transition density functions(or heat kernels) of the processes,a priori Hlder estimate and parabolic Harnack inequalities for their parabolic functions.In contrast to the second order elliptic differential operator case,the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.展开更多
The parabolic variational inequality for simulating the valuation of American option is used to analyze a continuous dependence of the solution with respect to the uncertain volatility parameter.Three kinds of the con...The parabolic variational inequality for simulating the valuation of American option is used to analyze a continuous dependence of the solution with respect to the uncertain volatility parameter.Three kinds of the continuity are proved,enabling us to employ the maximum range method for the uncertain parameter,under the condition that the criterion-functional has the corresponding property.展开更多
基金Project supported by the NSFC (10971019)Scientific Research Fund of Guangxi Education Department (201012MS067)USM Grant No.12.09.05
文摘This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.
文摘Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, it is proved there exists at least one solution.
基金supported by NSF (Grant No. DMS-0600206)supported by the Korea Science Engineering Foundation (KOSEF) Grant funded by the Korea government (MEST) (No. R01-2008-000-20010-0)supported by the Grant-in-Aid for Scientific Research (B) 18340027
文摘In this paper, we discuss necessary and sufficient conditions on jumping kernels for a class of jump-type Markov processes on metric measure spaces to have scale-invariant finite range parabolic Harnack inequality.
基金NSF of Guangxi(Grant No.2023GXNSFAA026085)Guangxi Science and Technology Department Specific Research Project of Guangxi for Research Bases and Talents(Grant No.AD23023001)+1 种基金NNSF of China Grant Nos.12071413,12111530282 the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECHthe Innovation Project of Guangxi University for Nationalities(Grant No.gxun-chxps202072)。
文摘The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department (Grant No.09ZB081)the Key Scientific Research Foundation of Xihua University (Grant No.Z0912611)+1 种基金Sichuan Youth Science & Technology Foundation (Grant No.2011JQ0003)the Fundamental Research Funds for the Central Universities
文摘In this paper, we establish a Liouville-type theorem for a system of higher-order parabolic inequalities by using the method of test functions and an integral estimate. As an application, we observe the Fujita blow-up phenomena for the corresponding parabolic system, which in particular fills up the gap in the recent result of Pang et. al. (Existence and nonexistence of global solutions for a higher-order semilinear parabolic system, Indiana Univ. Math. J., 55(2006), 1113-1134). Moreover, the importance of this observation is that we do not impose any regularity assumption on the initial data.
基金Supported by the National Natural Science Foundation of China(Grant No.11271087,No.61263006)Guangxi Scientific Experimental(China-ASEAN Research)Centre No.20120116
文摘We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximM monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.
基金partly supported by the Institut Camille Jordan ST-Etienne Universitythe projects Argentine ANPCyT PICTO Austral 2008 # 73 and SOARD-AFOSR (No. FA9550-10-1-0023)
文摘We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence of the optimal control and state systems associated to this family to a similar optimal control problem. This work solves the open problem left by the authors in IFIP TC7 CSMO2011.
文摘Iterative techniques for solving optimal control systems governed by parabolic varia-tional inequalities are presented. The techniques we use are based on linear finite elements method to approximate the state equations and nonlinear conjugate gradient methods to solve the discrete optimal control problem. Convergence results and numerical experiments are presented.
基金supported by National Science Foundation of USA(Grant No.DMS-0600206)
文摘We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently,a class of symmetric integro-differential operators).We focus on the sharp two-sided estimates for the transition density functions(or heat kernels) of the processes,a priori Hlder estimate and parabolic Harnack inequalities for their parabolic functions.In contrast to the second order elliptic differential operator case,the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.
基金supported by the Grant IAA 100190803 of the Academy of Sciences of the Czech Republic.
文摘The parabolic variational inequality for simulating the valuation of American option is used to analyze a continuous dependence of the solution with respect to the uncertain volatility parameter.Three kinds of the continuity are proved,enabling us to employ the maximum range method for the uncertain parameter,under the condition that the criterion-functional has the corresponding property.