The heat equation
Efficient high-order integral equation methods for the heat equation
... the heat kernel in arbitrary ...1D heat kernel and power ...the heat equation in both two and three ...the heat kernel and compress all local and history kernels only ...the heat ...
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On the stability of the heat equation with an initial condition
... The heat equation plays an important role in a number of fields of ...The heat equation is also connected with chemical diffusion, and it is sometimes called the diffusion ...
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Spherical Spline Solution of the Heat Equation
... the Heat Equation Victoria BARAMIDZE * Abstract We consider a spline approximation to the solution of the heat equation on the unit ...differential equation on the sphere is solved by ...
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5.4 The Heat Equation and Convection-Diffusion
... The Heat Equation and Convection-Diffusion The wave equation conserves ...The heat equation u t = u xx dissipates ...wave equation can be recovered by going backward in ...the ...
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Shape-from-shading using the heat equation
... the Heat Equation Antonio Robles-Kelly, Member, IEEE, and Edwin ...the heat equation to smooth the field of surface normals and the recovery of surface height using a low-di- mensional ...
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Algorithm Analysis of Numerical Solutions to the Heat Equation
... The Heat Equation with Dirichlet conditions conducting heat is analysed by employing the analytical method of solution where the method of Separation of Variables is ...same equation is then ...
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THE TWO VERSIONS OF THE DIRICHLET PROBLEM FOR THE HEAT EQUATION
... Abstract. There are two versions of the Dirichlet problem for the heat equation on an arbitrary open set in Euclidean space. For one of them, there is already a characterization of resolutivity in terms of ...
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Simultaneous determination of time-dependent coefficients in the heat equation
... In heat conduction for example, attention was paid to the unique solvability of one-dimensional inverse problems for the heat equation in the case when the unknown thermal coefficients are constant ...
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Determination of a source in the heat equation from integral observations
... the heat equation from integral observations is ...The heat source is sought in the form of a sum of two space- and time- dependent unknown components in order to ensure uniqueness of ...
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On a kind of time optimal control problem of the heat equation
... Abstract In this paper, we consider a kind of time-varying bang–bang property of time optimal boundary controls for the heat equation. The time-varying bang–bang property in the interior domain has been ...
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Hyers Ulam Rassias Stability for the Heat Equation
... dimensional heat equa- tion on an infinite ...of heat equation in with initial condition, in the sense of ...for heat equation on a finite ...
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Parameter estimation for the heat equation on perforated domains
... of heat through porous samples by use of solutions of a heat equation on a randomly perforated ...a heat equation on a perforated domain which was derived through limiting processes in ...
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Heat equation examples
... the heat equation we write as a PDE? The temperature function u(x, t) (or u(x, y, t) in two spatial dimensions) is the temperature within an object as a function of both position and ...time. Heat ...
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1 The 1-D Heat Equation
... basic Heat Problem Ref: Guenther & Lee § ...the heat equation occurs on the space-time “boundary”, ...the heat equation with some initial condition f (x) and BCs u (0, t), u (1, t), ...
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2D Heat Equation Code Report
... the heat equation in a 2D- Plate with some fixed initial conditions called "Dirichlet Conditions" to obtain a solution that describes the temperature of each node in space in any time within the ...
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On the spatial dynamics of the solution to the stochastic heat equation
... R × R i → R . We write g as an inhomogeneous transition kernel in order to emphasise that the method works for more general PDE problems than the heat equation. However for some ex- plicit calculations we ...
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Invariant Solutions of Two Dimensional Heat Equation
... ( x t u , , ) ( → x + as t , + bs u , ) , s ∈ (2) is a symmetry group, because if the function u = f x ( ) is a solution, then the function u = f x ( − as t , − bs ) is also a solution to the heat ...
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A multi layer extension of the stochastic heat equation
... The outline of the paper is as follows. In the next section we provide some background on non-intersecting Brownian motions and their bridges. Following this we study the analogue of the partition functions when the ...
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Particular Solution to a Time-Fractional Heat Equation
... IBVP Heat Equation Solution The standard heat equation is ∂u ∂t = ∂ ∂x 2 u 2 ...this equation the temperature is represented by u, which is a function of time, t, and space, ...the ...
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Solving the backward heat equation on the unit sphere
... (Received 26 February 2015; revised 8 January 2016) Abstract We consider an inverse problem for the heat equation on the unit sphere in which the final (current) temperature on the sphere is given, and the ...
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