In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic be...In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.展开更多
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using...In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.展开更多
The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose bounda...The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.展开更多
The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed ...The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.展开更多
A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptot...A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of solution for the initial boundary value problems are studied.展开更多
The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are...The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are studied.The uniform validity of its asymptotic expansion is proved by using the fixed point theorem.展开更多
A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer...A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.展开更多
For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the...For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.展开更多
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence...The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.展开更多
We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary i...We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.展开更多
基金Supported by the National Natural Science Foundation of China (10471039) the Natural Science Foundation of Zhejiang Province (102009)the Natural Science Foundation of Huzhou City (2004SZX0707).
文摘In this paper the method and technique of the diagonalization are employed to transform a vector second-order nonlinear system into two first-order approximate diagonalized systems. The existence and the asymptotic behavior of the solutions are obtained for a vector second-order nonlinear Robin problem of singular perturbation type.
基金Supported by the Natural Science Foundations of Zhejiang Province(102009) Supported by the Zhejiang Educational Offlce(20020305) Supported by Huzhou Teacher's College(02101A)
文摘In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.
文摘The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called “superformula” introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
基金Supported by the National Natural Science Foundation of China (No. 10671064 and No.10971061)the Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.
基金Supported by the National Natural Science Foundation of China (90111011 and 10471039)the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Insitutes of Shanghai Municipal Education Commission (N.E03004) and the Natural Science Foundation of Zhejiang (Y604127).
文摘A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of solution for the initial boundary value problems are studied.
基金Supported by the National Natural Science Foundation of China(11271247)the Excellent Youth Talented Project of the Colleges and Universities in Anhui Province(gxyqZD2016520)+1 种基金the Key Project for Teaching Research in Anhui Province(2017jyxm0591,2018jyxm0594)the Key Project for Natural Science Research in Anhui Province(KJ2015A347,KJ2019A1300).
文摘The singularly perturbed Robin boundary value problem for the higher order elliptic equation is considered.Under suitable conditions,the existence and asymptotic behavior of solution to the boundary value problems are studied.The uniform validity of its asymptotic expansion is proved by using the fixed point theorem.
基金supported by the National Natural Science Foundation of China (40876010)the LASG State Key Laboratory Special Fund+3 种基金the Natural Science Foundation of Zhejiang Province (Y6110502)the Foundation of the Education Department of Fujian Province (JA10288)the Natural Science Foundation from the Education Bureau of Anhui Province (KJ2011A135KJ2011Z003)
文摘A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.
基金supported by National Natural Science Foundation of China(Grant Nos.11226332,41204082 and 11071067)the China Postdoctoral Science Foundation(Grant No.2011M501295)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120162120036)the Construct Program of the Key Discipline in Hunan Province
文摘For the Poisson equation with Robin boundary conditions,by using a few techniques such as orthogonal expansion(M-type),separation of the main part and the finite element projection,we prove for the first time that the asymptotic error expansions of bilinear finite element have the accuracy of O(h3)for u∈H3.Based on the obtained asymptotic error expansions for linear finite elements,extrapolation cascadic multigrid method(EXCMG)can be used to solve Robin problems effectively.Furthermore,by virtue of Richardson not only the accuracy of the approximation is improved,but also a posteriori error estimation is obtained.Finally,some numerical experiments that confirm the theoretical analysis are presented.
基金Important Study Project of the NationalNatural Science F oundation of China( No.90 2 110 0 4),and"Hun-dred Talents Project"of Chinese Academy of Sciences
文摘The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
文摘We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.
基金Supported by the National Natural Science Foundation of China(40876010,49906013)the Strategic Priority Research Program-Climate Change:Carbon Budget and Relevant Issues of the Chinese Academy of Science(XDA01020304)+1 种基金the Natural Science Foundation of Jiangsu Province(BK20110420)the Natural Science Foundation from the Education Bureau of Anhui Province(KJ2010A128,KJ2010B360)
基金the National Natural Science Foundation of China (40531006 and 10471039)the National Key Project for Basics Research (2003CB415101-03 and 2004CB418304)+1 种基金the Key Project of the Chinese Academy of Sciences (KZCX3-SW-221)in part by E-Insitutes of Shanghai Municipal Education Commission (N.E03004).
