The Experts below are selected from a list of 147 Experts worldwide ranked by ideXlab platform
Hiroko Morimoto - One of the best experts on this subject based on the ideXlab platform.
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heat convection equation with Nonhomogeneous Boundary Condition
Funkcialaj Ekvacioj, 2010Co-Authors: Hiroko MorimotoAbstract:We consider the stationary heat convection equations and the time periodic heat convection equations (Boussinesq approximation) with non-homogeneous Boundary Condition, and obtain the existence result similar to the Navier-Stokes equations' case.The Boundary value for the fluid velocity should satisfy so-called general outflow Condition (GOC). For the 2 or 3 dimensional bounded domain, the existence of the solution can be shown if the Boundary Condition satisfies the stringent outflow Condition (SOC). Similarly to the Navier-Stokes equations, we obtain the existence result for the 2 dimensional symmetric domain and symmetric data with the Boundary value satisfying only (GOC).
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time periodic navier stokes flow with Nonhomogeneous Boundary Condition
Journal of Mathematical Sciences-the University of Tokyo, 2009Co-Authors: Hiroko MorimotoAbstract:It is known that the Navier-Stokes initial Boundary value problem for non-homogeneous Boundary Condition has a unique local solution (e.g., O. A. Ladyzhenskaya(5)). Nevertheless, it seems to the author that there is no results for the periodic problem with non-homogeneous Boundary Condition satisfying the general outflow Condition. We consider the periodic problem for the Navier-Stokes equations in a two dimensional bounded domain. In case of a symmet- ric domain, we obtain a periodic weak solution for symmetric Boundary values satisfying only the general outflow Condition.
Shengquan Xiang - One of the best experts on this subject based on the ideXlab platform.
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Local exponential stabilization for a class of Korteweg–de Vries equations by means of time-varying feedback laws
Analysis & PDE, 2017Co-Authors: Jean-michel Coron, Ivonne Rivas, Shengquan XiangAbstract:We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet Boundary Conditions at the end-points of the interval, a Neumann Nonhomogeneous Boundary Condition at the right end-point which is the control. We build a class of time-varying feedback laws for which the solutions of the closed-loop systems with small initial data decay exponentially to 0. We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.
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Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws
Analysis & PDE, 2017Co-Authors: Jean-michel Coron, Ivonne Rivas, Shengquan XiangAbstract:We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet Boundary Conditions at the end-points of the interval, a Neumann Nonhomogeneous Boundary Condition at the right end-point which is the control. We build a class of time-varying feedback laws for which the solutions of the closed-loop systems with small initial data decay exponentially to 0. We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.
Raj Narayan Dhara - One of the best experts on this subject based on the ideXlab platform.
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existence and uniqueness of the solution of linear degenerate pdes in weighted sobolev space with Nonhomogeneous Boundary Condition
Mathematical Methods in The Applied Sciences, 2017Co-Authors: Raj Narayan DharaAbstract:We prove the existence and uniqueness of solution to the Nonhomogeneous degenerate elliptic PDE of second order with Boundary data in weighted Orlicz-Slobodetskii space. Our goal is to consider the possibly general assumptions on the involved constraints: the class of weights, the Boundary data, and the admitted coefficients. We also provide some estimates on the spectrum of our degenerate elliptic operator.
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On proper formulation of Boundary Condition for degenerated PDEs when trace embedding theorems are missing and application to Nonhomogeneous BVPs
Complex Variables and Elliptic Equations, 2016Co-Authors: Raj Narayan Dhara, Agnieszka KałamajskaAbstract:We propose certain interpretation of Boundary Conditions on , the Boundary of , when f belongs to the weighted Sobolev space subordinated to the integrable weight and g is defined on , where is a given domain. It may happen that the trace embedding theorems are missing. Our proposed interpretation requires to have defined an extension operator , where X is the relevant function space of functions defined on . We show that the proposed interpretation does not depend on the choice of the extension operator . Moreover, we apply our result to obtain existence and uniqueness of solutions to an example of the Boundary value problem involving degenerated p-Laplacian with Nonhomogeneous Boundary Condition. Existence of the extension operator within the class of weights when is certain weighted Slobodetskii space and is a Lipschitz Boundary domain is confirmed by our previous results.
Jean-michel Coron - One of the best experts on this subject based on the ideXlab platform.
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Local exponential stabilization for a class of Korteweg–de Vries equations by means of time-varying feedback laws
Analysis & PDE, 2017Co-Authors: Jean-michel Coron, Ivonne Rivas, Shengquan XiangAbstract:We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet Boundary Conditions at the end-points of the interval, a Neumann Nonhomogeneous Boundary Condition at the right end-point which is the control. We build a class of time-varying feedback laws for which the solutions of the closed-loop systems with small initial data decay exponentially to 0. We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.
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Local exponential stabilization for a class of Korteweg-de Vries equations by means of time-varying feedback laws
Analysis & PDE, 2017Co-Authors: Jean-michel Coron, Ivonne Rivas, Shengquan XiangAbstract:We study the exponential stabilization problem for a nonlinear Korteweg-de Vries equation on bounded interval in cases where the linearized control system is not controllable. The system has Dirichlet Boundary Conditions at the end-points of the interval, a Neumann Nonhomogeneous Boundary Condition at the right end-point which is the control. We build a class of time-varying feedback laws for which the solutions of the closed-loop systems with small initial data decay exponentially to 0. We present also results on the well-posedness of the closed-loop systems for general time-varying feedback laws.
Dennis S. Bernstein - One of the best experts on this subject based on the ideXlab platform.
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State Space Modeling of an Acoustic Duct with an nted Speaker
1996Co-Authors: Ravinder Venugopal, Dennis S. BernsteinAbstract:This paper develops a state space model of an acoustic duct with end-mounted speakers. The initial model formulation introduces the forcing term as a Boundary Condition. The shifted particle velocity is then defined to transform the Nonhomogeneous Boundary Condition to a homogeneous Boundary Condition and thus develop the state space model. It is shown that the speaker and acoustic duct interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker baffle. The interaction between the speaker and acoustic dynamics is studied using positive real closed-loop feedback analysis, and shifts in the modal frequencies of the duct due to the presence of the end-mounted speaker -are predicted.
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State space modeling of an acoustic duct with an end-mounted speaker
Proceeding of the 1996 IEEE International Conference on Control Applications IEEE International Conference on Control Applications held together with , 1Co-Authors: Ravinder Venugopal, Dennis S. BernsteinAbstract:This paper develops a state space model of an acoustic duct with end-mounted speakers. The initial model formulation introduces the forcing term as a Boundary Condition. The shifted particle velocity is then defined to transform the Nonhomogeneous Boundary Condition to a homogeneous Boundary Condition and thus develop the state space model. It is shown that the speaker and acoustic duct interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker baffle. The interaction between the speaker and acoustic dynamics is studied using positive real closed-loop feedback analysis, and shifts in the modal frequencies of the duct due to the presence of the end-mounted speaker are predicted.