Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bou...Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.展开更多
In this paper,we define a kind of new Sobolev spaces,the relative Sobolev spaces Wk,p0(Ω,∑).Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed.By utilizing the...In this paper,we define a kind of new Sobolev spaces,the relative Sobolev spaces Wk,p0(Ω,∑).Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed.By utilizing the ideal of the generalized inverse of an operator,we introduce the generalized solution of the ill-posed boundary problem.Eventually,the connection between the generalized inverse and the generalized solution is studied.In this way,the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.展开更多
基金China State Major Key Project for Basic Researches
文摘Combining difference method and boundary integral equation method,we propose a new numerical method for solving initial-boundary value problem of second order hyperbolic partial differential equations defined on a bounded or unbounded domain in R~3 and obtain the error estimates of the approximate solution in energy norm and local maximum norm.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171087)the Science Foundation of Jiangsu Province(Grant No.01KJD110010).
文摘In this paper,we define a kind of new Sobolev spaces,the relative Sobolev spaces Wk,p0(Ω,∑).Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed.By utilizing the ideal of the generalized inverse of an operator,we introduce the generalized solution of the ill-posed boundary problem.Eventually,the connection between the generalized inverse and the generalized solution is studied.In this way,the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.
