In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi e...In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.展开更多
Let u be a solution to second order elliptic equations in Dini domains, a direct and elementary proof of the doubling property for u 2 over balls centered at points in the domain is presented. Moreover, under the zero...Let u be a solution to second order elliptic equations in Dini domains, a direct and elementary proof of the doubling property for u 2 over balls centered at points in the domain is presented. Moreover, under the zero Dirichlet boundary condition, the unique continuation at the boundary for Dini domains has been proved.展开更多
In this paper, we first propose a metamaterial structure by etching the same two interdigital fingers on the upper ground of quarter mode substrate integrated waveguide（QMSIW）. The simulated results show that the pr...In this paper, we first propose a metamaterial structure by etching the same two interdigital fingers on the upper ground of quarter mode substrate integrated waveguide（QMSIW）. The simulated results show that the proposed QMSIWbased metamaterial has a continuous phase constant changing from negative to positive values within its passband. A periodic leaky-wave antenna（LWA）, which consists of 11 QMSIW-based metamaterial unit cells, is designed, fabricated,and measured. The measured results show that the fabricated antenna achieves a continuous beam scanning property from backward-43° to forward ＋32° over an operating frequencyrange of 8.9 GHz–11.8 GHz with return loss better than 10 d B.The measured antenna gain keeps consistent with the variation of less than 2 d B over the operating frequency range with a maximum gain of 12 d B. Besides, the measured and simulated results are in good agreement with each other, indicating the significance and effectiveness of this method.展开更多
The unique continuation property has been extensively studied for partial differential equations.Nevertheless,this fundamental concept has not yet received sufficient investigation when it comes to stochastic partial ...The unique continuation property has been extensively studied for partial differential equations.Nevertheless,this fundamental concept has not yet received sufficient investigation when it comes to stochastic partial differential equations.Particularly,to the best of our knowledge,there is no published work addressing the strong unique continuation property of stochastic partial differential equations.In this paper,we obtain a strong unique continuation property for stochastic parabolic equations.To achieve that,we establish a new stochastic version of the Carleman estimate.展开更多
In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials.Our argument is to establish some Hardy-Rellich type inequalities wi...In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials.Our argument is to establish some Hardy-Rellich type inequalities with boundary terms and introduce an Almgren’s type frequency function to show some doubling conditions for the solutions to the above-mentioned equations.展开更多
In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for ...In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for bounded linear operators.It is found that these results depend strongly on a continuous extension property,which is always true in the classical archimedean case,but may fail to hold for the non-archimedean setting.Several counterexamples are given to show that our results are sharp in some sense.展开更多
基金supported by NNSFC(11001219,10925104)the Scientific Research Program Funded by Shaanxi Provincial Education Department(2010JK860)
文摘In this article, the unique continuation and persistence properties of solutions of the 2-component Degasperis-Procesi equations are discussed. It is shown that strong solutions of the 2-component Degasperis-Procesi equations, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if they also decay exponentially at a later time.
文摘Let u be a solution to second order elliptic equations in Dini domains, a direct and elementary proof of the doubling property for u 2 over balls centered at points in the domain is presented. Moreover, under the zero Dirichlet boundary condition, the unique continuation at the boundary for Dini domains has been proved.
基金Project supported by the National Natural Science Foundation of China(Grant No.61372034)
文摘In this paper, we first propose a metamaterial structure by etching the same two interdigital fingers on the upper ground of quarter mode substrate integrated waveguide（QMSIW）. The simulated results show that the proposed QMSIWbased metamaterial has a continuous phase constant changing from negative to positive values within its passband. A periodic leaky-wave antenna（LWA）, which consists of 11 QMSIW-based metamaterial unit cells, is designed, fabricated,and measured. The measured results show that the fabricated antenna achieves a continuous beam scanning property from backward-43° to forward ＋32° over an operating frequencyrange of 8.9 GHz–11.8 GHz with return loss better than 10 d B.The measured antenna gain keeps consistent with the variation of less than 2 d B over the operating frequency range with a maximum gain of 12 d B. Besides, the measured and simulated results are in good agreement with each other, indicating the significance and effectiveness of this method.
基金supported by National Natural Science Foundation of China(Grants Nos.12025105,11931011,and 11971334)the New Cornerstone Science Foundation,and the Science Development Project of Sichuan University(Grants Nos.2020SCUNL201,2020SCUNL101,and 2024SCU12091)。
文摘The unique continuation property has been extensively studied for partial differential equations.Nevertheless,this fundamental concept has not yet received sufficient investigation when it comes to stochastic partial differential equations.Particularly,to the best of our knowledge,there is no published work addressing the strong unique continuation property of stochastic partial differential equations.In this paper,we obtain a strong unique continuation property for stochastic parabolic equations.To achieve that,we establish a new stochastic version of the Carleman estimate.
基金supported by National Natural Science Foundation of China(Grant No.11401310)supported by National Natural Science Foundation of China(Grant No.11531005).
文摘In this paper we prove the strong unique continuation property for a class of fourth order elliptic equations involving strongly singular potentials.Our argument is to establish some Hardy-Rellich type inequalities with boundary terms and introduce an Almgren’s type frequency function to show some doubling conditions for the solutions to the above-mentioned equations.
基金supported by National Natural Science Foundation of China(Grant Nos.10831007,60821091 and 60974035)National Basic Research Program of China(Grant No.2011CB808002),Independent Innovation Foundation of Shandong Universitythe project MTM2008-03541 of the Spanish Ministry of Science and Innovation
文摘In this paper,we establish some range inclusion theorems for non-archimedean Banach spaces over general valued fields.These theorems provide close relationship among range inclusion,majorization and factorization for bounded linear operators.It is found that these results depend strongly on a continuous extension property,which is always true in the classical archimedean case,but may fail to hold for the non-archimedean setting.Several counterexamples are given to show that our results are sharp in some sense.
