This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on ...This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.展开更多
In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are deriv...In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.展开更多
In this paper, we consider the identification of parameters in parabolic equations with nonlinearity. Some approximation processes for the identification problem are given. Our results improve and generalize the previ...In this paper, we consider the identification of parameters in parabolic equations with nonlinearity. Some approximation processes for the identification problem are given. Our results improve and generalize the previous results.展开更多
文摘This paper establishes a global Carleman inequality of parabolic equations with mixed boundary conditions and an estimate of the solution. Further, we prove exact controllability of the equation by controls acting on an arbitrarily given subdomain or subboundary.
文摘In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.
基金supported by the National Natural Science Foundation of China (10671211)the Scientific Research Foundation of Hunan Provincial Educational Department (09C852)
文摘In this paper, we consider the identification of parameters in parabolic equations with nonlinearity. Some approximation processes for the identification problem are given. Our results improve and generalize the previous results.