The Experts below are selected from a list of 2358 Experts worldwide ranked by ideXlab platform
Yuriy Povstenko - One of the best experts on this subject based on the ideXlab platform.
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fundamental solutions to the fractional heat conduction equation in a ball under Robin Boundary Condition
Open Mathematics, 2014Co-Authors: Yuriy PovstenkoAbstract:The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin Boundary Condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the Boundary, and the physical Condition with the prescribed linear combination of values of temperature and values of the heat flux at the Boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.
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Fundamental Solutions to Robin Boundary-Value Problems for the Time-Fractional Heat-Conduction Equation in a Half Line
Journal of Mathematical Sciences, 2013Co-Authors: Yuriy PovstenkoAbstract:The time-fractional heat-conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in a half line. Two types of Robin Boundary Condition are examined: the mathematical Condition with prescribed linear combination of the values of temperature and the values of its normal derivative and the physical Condition with prescribed linear combination of the values of temperature and the values of heat flux on the Boundary of the domain. These two types of Robin Boundary Condition coincide only for the classical heat-conduction equation.
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time fractional heat conduction in an infinite medium with a spherical hole under Robin Boundary Condition
Fractional Calculus and Applied Analysis, 2013Co-Authors: Yuriy PovstenkoAbstract:The time-fractional heat conduction equation with the Caputo derivative of the order 0 < α ≤ 2 is considered in an infinite medium with a spherical hole in the central symmetric case under two types of Robin Boundary Condition: the mathematical one with the prescribed linear combination of the values of temperature and the values of its normal derivative at the Boundary and the physical Condition with the prescribed linear combination of the values of temperature and the values of the heat flux at the Boundary. The integral transforms techniques are used. Several particular cases of the obtained solutions are analyzed. The numerical results are illustrated graphically.
Jin Zhang - One of the best experts on this subject based on the ideXlab platform.
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asymptotic behaviors of radially symmetric solutions to diffusion problems with Robin Boundary Condition in exterior domain
Nonlinear Analysis-real World Applications, 2018Co-Authors: Jin ZhangAbstract:Abstract In this paper we study nonlinear diffusion problems of the form u t = Δ u + f ( u ) with Robin Boundary Condition in exterior domain and heterogeneous environment where f ( u ) is a bistable term. First we prove that the radially symmetric solution converges to its equilibrium locally uniformly in the exterior domain. Then we discuss the existence of some certain equilibrium and obtain a spreading–transition–vanishing trichotomy result. Finally the behavior changes with respect to the initial data are presented.
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asymptotic behavior of solutions of a reaction diffusion equation with inhomogeneous Robin Boundary Condition and free Boundary Condition
Nonlinear Analysis-real World Applications, 2016Co-Authors: Jin ZhangAbstract:Abstract This paper studies the long time behavior of solutions of a reaction–diffusion model with inhomogeneous Robin Boundary Condition at x = 0 and free Boundary Condition at x = h ( t ) . We prove that, for the initial data u 0 = σ ϕ , there exists σ ∗ ⩾ 0 such that u ( ⋅ , t ) converges to a positive stationary solution which tends to 1 as x → ∞ locally uniformly in [ 0 , ∞ ) when σ > σ ∗ . In the case of σ ⩽ σ ∗ the solution u ( ⋅ , t ) converges to the ground state V ( ⋅ − z ) where V is the unique even positive solution of V ″ + f ( V ) = 0 subject to V ( ∞ ) = 0 and z is the root of a V ′ ( − z ) − ( 1 − a ) V ( − z ) = b . The asymptotic behavior of the solutions is quite different from the homogeneous case b = 0 .
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Asymptotic behavior of solutions of a reaction–diffusion equation with inhomogeneous Robin Boundary Condition and free Boundary Condition
Nonlinear Analysis-real World Applications, 2016Co-Authors: Jin ZhangAbstract:Abstract This paper studies the long time behavior of solutions of a reaction–diffusion model with inhomogeneous Robin Boundary Condition at x = 0 and free Boundary Condition at x = h ( t ) . We prove that, for the initial data u 0 = σ ϕ , there exists σ ∗ ⩾ 0 such that u ( ⋅ , t ) converges to a positive stationary solution which tends to 1 as x → ∞ locally uniformly in [ 0 , ∞ ) when σ > σ ∗ . In the case of σ ⩽ σ ∗ the solution u ( ⋅ , t ) converges to the ground state V ( ⋅ − z ) where V is the unique even positive solution of V ″ + f ( V ) = 0 subject to V ( ∞ ) = 0 and z is the root of a V ′ ( − z ) − ( 1 − a ) V ( − z ) = b . The asymptotic behavior of the solutions is quite different from the homogeneous case b = 0 .
Peixin Zhang - One of the best experts on this subject based on the ideXlab platform.
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global classical solutions to 1d full compressible navier stokes equations with the Robin Boundary Condition on temperature
Nonlinear Analysis-real World Applications, 2019Co-Authors: Peixin ZhangAbstract:Abstract In this paper, we consider the initial Boundary value problem for the one-dimensional Navier–Stokes equations for viscous compressible and heat-conducting fluids in a bounded domain with the Robin Boundary Condition on temperature. There are few results until now about global existence of regular solutions to the full Navier–Stokes equations with the Robin Boundary Condition on temperature. By the analysis of the effect of Boundary dissipation, we derive the global existence of classical solution to the corresponding initial Boundary value problem with large initial data and vacuum. This result could be viewed as the first one on the global well-posedness of classical solutions to the full Navier–Stokes equations in a bounded domain with the Robin Boundary Condition on temperature.
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Global classical solutions to 1D full compressible Navier–Stokes equations with the Robin Boundary Condition on temperature
Nonlinear Analysis-real World Applications, 2019Co-Authors: Peixin ZhangAbstract:Abstract In this paper, we consider the initial Boundary value problem for the one-dimensional Navier–Stokes equations for viscous compressible and heat-conducting fluids in a bounded domain with the Robin Boundary Condition on temperature. There are few results until now about global existence of regular solutions to the full Navier–Stokes equations with the Robin Boundary Condition on temperature. By the analysis of the effect of Boundary dissipation, we derive the global existence of classical solution to the corresponding initial Boundary value problem with large initial data and vacuum. This result could be viewed as the first one on the global well-posedness of classical solutions to the full Navier–Stokes equations in a bounded domain with the Robin Boundary Condition on temperature.
Dmitry Shepelsky - One of the best experts on this subject based on the ideXlab platform.
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Robin Boundary Condition and shock problem for the focusing nonlinear schrodinger equation
Journal of Nonlinear Mathematical Physics, 2015Co-Authors: Spyridon Kamvissis, Dmitry Shepelsky, Lech ZielinskiAbstract:We consider the initial Boundary value (IBV) problem for the focusing nonlinear Schrodinger equation in the quarter plane x>0, t >0 in the case of periodic initial data, u(x,0) = α exp(−2iβx) (or asymptotically periodic, u(x, 0) =α exp(−2iβx)→0 as x→∞), and a Robin Boundary Condition at x = 0: ux(0, t)+qu(0, t) = 0, q ≠ 0. Our approach is based on the unified transform (the Fokas method) combined with symmetry considerations for the corresponding Riemann-Hilbert (RH) problems. We present the representation of the solution of the IBV problem in terms of the solution of an associated RH problem. This representation also allows us to determine an initial value (IV) problem, of a shock type, a solution of which being restricted to the half-line x > 0 is the solution of the original IBV problem. In the case β 0,...
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Robin Boundary Condition and shock problem for the focusing nonlinear schr odinger equation
arXiv: Exactly Solvable and Integrable Systems, 2014Co-Authors: Spyridon Kamvissis, Dmitry Shepelsky, Lech ZielinskiAbstract:We consider the initial Boundary value (IBV) problem for the focusing nonlinear Schr\"odinger equation in the quarter plane $x>0,t>0$ in the case of periodic initial data (at $t=0$) and a Robin Boundary Condition at $x=0$. Our approach is based on the simultaneous spectral analysis of the Lax pair equations combined with symmetry considerations for the corresponding Riemann-Hilbert problems. A connection between the original IBV problem and an associated initial value (IV) problem is established.
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initial Boundary value problem for the focusing nonlinear schrodinger equation with Robin Boundary Condition half line approach
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2013Co-Authors: Dmitry ShepelskyAbstract:We consider the initial Boundary value problem for the focusing nonlinear Schrodinger equation in the quarter plane x >0, t >0 in the case of decaying initial data (for t =0, as ![Graphic][1] ) and the Robin Boundary Condition at x =0. We revisit the approach based on the simultaneous spectral analysis of the Lax pair equations and show that the method can be implemented without any a priori assumptions on the long-time behaviour of the Boundary values. [1]: /embed/inline-graphic-1.gif
Gen Nakamura - One of the best experts on this subject based on the ideXlab platform.
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born series for the photon diffusion equation perturbing the Robin Boundary Condition
arXiv: Mathematical Physics, 2020Co-Authors: Manabu Machida, Gen NakamuraAbstract:The photon diffusion equation is solved making use of the Born series for the Robin Boundary Condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. It is shown that in this case the Born series converges regardless the value of the impedance term in the Robin Boundary Condition.
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born series for the photon diffusion equation perturbing the Robin Boundary Condition
Journal of Mathematical Physics, 2020Co-Authors: Manabu Machida, Gen NakamuraAbstract:The photon diffusion equation is solved making use of the Born series for the Robin Boundary Condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. It is shown that in this case, the Born series converges regardless the value of the impedance term in the Robin Boundary Condition.The photon diffusion equation is solved making use of the Born series for the Robin Boundary Condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. It is shown that in this case, the Born series converges regardless the value of the impedance term in the Robin Boundary Condition.
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born series for the Robin Boundary Condition
arXiv: Mathematical Physics, 2017Co-Authors: Manabu Machida, Gen NakamuraAbstract:We solve the diffusion equation by constructing the Born series for the Robin Boundary Condition. We develop a general theory for arbitrary domains with smooth enough boundaries and explore the convergence. The proposed Born series is validated by numerical calculation in the three-dimensional half space. We show that in this case the Born series converges regardless the value of the impedance term in the Robin Boundary Condition. We point out that the solution from the so-called extrapolated Boundary Condition does not have such convergence to the exact solution.
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reconstruction of an unknown cavity with Robin Boundary Condition inside a heat conductor
Inverse Problems, 2015Co-Authors: Gen Nakamura, Haibing WangAbstract:Active thermography is a non-destructive testing technique to detect the internal structure of a heat conductor, which is widely applied in industrial engineering. In this paper, we consider the problem of identifying an unknown cavity with Robin Boundary Condition inside a heat conductor from Boundary measurements. To set up the inverse problem mathematically, we first state the corresponding forward problem and show its well-posedness in an anisotropic Sobolev space by the integral equation method. Then, taking the Neumann-to-Dirichlet map as mathematically idealized measurement data for the active thermography, we present a linear sampling method for reconstructing the unknown Robin-type cavity and give its mathematical justification by using the layer potential argument. In addition, we analyze the indicator function used in this method and show its pointwise asymptotic behavior by investigating the reflected solution of the fundamental solution. Based on our asymptotic analysis, we can establish a pointwise reconstruction scheme for the Boundary of the cavity, and can also know the distance to the unknown cavity as we probe it from its inside. The numerical results are presented to show the performance of the reconstruction scheme and the asymptotic behavior.
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reconstruction of an unknown cavity with Robin Boundary Condition inside a heat conductor
arXiv: Mathematical Physics, 2015Co-Authors: Gen Nakamura, Haibing WangAbstract:Active thermography is a non-destructive testing technique to detect the internal structure of a heat conductor, which is widely applied in industrial engineering. In this paper, we consider the problem of identifying an unknown cavity with Robin Boundary Condition inside a heat conductor from Boundary measurements. To set up the inverse problem mathematically, we first state the corresponding forward problem and show its well-posedness in an anisotropic Sobolev space by the integral equation method. Then, taking the Neumann-to-Dirichlet map as mathematically idealized measured data for the active thermography, we present a linear sampling method for reconstructing the unknown Robin-type cavity and give its mathematical justification by using the layer potential argument. In addition, we analyze the indicator function used in this method and show its pointwise asymptotic behavior by investigating the reflected solution of the fundamental solution. From our asymptotic analysis, we can establish a pointwise reconstruction scheme for the Boundary of the cavity, and can also know the distance to the unknown cavity as we probe it from its inside.
