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Posts Tagged ‘HEAT equation’

Non-polynomial spline method for fractional diffusion equation






The one-dimensional fractional diffusion equation is studied systematically using the non-polynomial spline method. The Caputo fractional derivative is used for formulation. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of equation. An effective and easy-to-use method for solving such equations is needed. [ABSTRACT FROM AUTHOR]


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A novel approach for the estimation of soil ground heat flux

Abstract: Most conventional numerical schemes for soil ground heat flux estimation rely on the knowledge of the temporal evolution of soil temperature. Here we propose and test a novel scheme, which requires no information on soil temperatures to supplement the flux plate measurement. The proposed method is based on the fundamental solution of the one-dimensional heat equation and Duhamel”s principle for the incorporation of inhomogeneous boundary conditions. Being completely independent of the soil temperature, the new scheme therefore avoids a potential source of error in measurements and in heat storage calculation. The only thermal property involved in the new scheme is the thermal diffusivity of the soil, which is a weak function of soil water content and can be approximated as constant with reasonable accuracy. For validation, the proposed method is compared to the conventional approach using a canonical one-dimensional heat conduction problem, as well as real field measurements. Results of the comparison highlight that the new model is robust and capable of preserving the good accuracy of the conventional approach with reduced input information. In addition, the effect of inclusion of the heat storage term in the ground heat flux is evaluated in the context of surface energy balance closure for field measurements. [Copyright &y& Elsevier]

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Norms of nonnegative schrödinger heat semigroup and the large time behavior of hot spots

Abstract: This paper is concerned with the Cauchy problem for the heat equation with a potential where , , , and is a smooth, nonpositive, and radially symmetric function having quadratic decay at the space infinity. In this paper we assume that the Schrödinger operator is nonnegative on , and give the exact power decay rates of norm of the solution of (P) as . Furthermore we study the large time behavior of the solution of (P) and its hot spots. [Copyright &y& Elsevier]

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On a stochastic singular diffusion equation in

Abstract: We establish the existence and uniqueness of a strong solution to the Cauchy problem for a singular diffusion equation with random noise in with initial data in with bounded variation or in . We also prove the existence of an invariant measure and extinction of a solution in finite time. [Copyright &y& Elsevier]

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