In this paper we consider the existence of the solution to the inverse problem identifying the function pair (q, u) satisfyingUsing the fixed point theory, we obtain the definite answer to the above-mentioned problem ...In this paper we consider the existence of the solution to the inverse problem identifying the function pair (q, u) satisfyingUsing the fixed point theory, we obtain the definite answer to the above-mentioned problem under milder conditions. Similar results are also obtained for the elliptic and hyperbolic operators, respectively.展开更多
We consider to identify the parameters.which are functions of spatial and or time variables,in a quasi-linear parabolic equation.First,we prove that the solution of the parabolic equation is a smooth function with re...We consider to identify the parameters.which are functions of spatial and or time variables,in a quasi-linear parabolic equation.First,we prove that the solution of the parabolic equation is a smooth function with respect to the parameters,and then we give a modified Newton-Kantorovich iteration regularity method(NKR) to construct the solution of the inverse problem of the partial differential equation.Secondly,we give a proof of convergence for NKR. Finally,we give a computational example to show that the sequence generated by NKR does converge to the real solution of the inverse problem when the initial guess is close to it.展开更多
In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved u...In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.展开更多
文摘In this paper we consider the existence of the solution to the inverse problem identifying the function pair (q, u) satisfyingUsing the fixed point theory, we obtain the definite answer to the above-mentioned problem under milder conditions. Similar results are also obtained for the elliptic and hyperbolic operators, respectively.
文摘We consider to identify the parameters.which are functions of spatial and or time variables,in a quasi-linear parabolic equation.First,we prove that the solution of the parabolic equation is a smooth function with respect to the parameters,and then we give a modified Newton-Kantorovich iteration regularity method(NKR) to construct the solution of the inverse problem of the partial differential equation.Secondly,we give a proof of convergence for NKR. Finally,we give a computational example to show that the sequence generated by NKR does converge to the real solution of the inverse problem when the initial guess is close to it.
文摘In this paper the inverse problem of determining the source term, which is independent of the time variable, of a linear, uniformly-parabolic equation is investigated. The uniqueness of the inverse problem is proved under mild assumptions by using the orthogonality method and an elimination method. The existence of the inverse problem is proved by means of the theory of solvable operators between Banach spaces; moreover, the continuous dependence on measurement of the solution to the inverse problem is also proved.
