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Ulam-Hyers stability of a parabolic partial differential equation
Demonstratio Mathematica, 2019 The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability.
Marian Daniela +2 more
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On a parabolic partial differential equation and system modeling a production planning problem
Electronic Research Archive, 2022 We consider a parabolic partial differential equation and system derived from a production planning problem dependent on time. Our goal is to find a closed-form solution for the problem considered in our model.
Dragos-Patru Covei
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Postprocessing for Stochastic Parabolic Partial Differential Equations [PDF]
SIAM Journal on Numerical Analysis, 2007 We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce postprocessing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [G. J. Lord and J. Rougemont, IMA J. Numer. Anal., 24 (2004), pp. 587-604] and use an
Gabriel J. Lord, Tony Shardlow
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Minimal solutions to a class of parabolic partial differential equations [PDF]
Proceedings of the American Mathematical Society, 1969 The problem considered is that of minimizing a linear function \(L(u(t^1,x))\) on the class of linear functionals satisfying (*) \(u_t = Eu\) and certain initial and boundary conditions on a set \(T\times \Omega_0\) where \(T= [t^0,t^1]\), \(\Omega_0\) is a compact subset in Euclidean space and \(E\in\mathcal E\), a set of linear elliptic operators ...
T. Guinn, Edward M. Landesman
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Positive Solutions of a Nonlinear Parabolic Partial Differential Equation [PDF]
Abstract and Applied Analysis, 2014 We deal with the existence and uniqueness of positive solutions to a class of nonlinear parabolic partial differential equations, by using some fixed point theorems for mixed monotone operators with perturbation.
Chengbo Zhai, Shunyong Li
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The Method of Lines for Parabolic Partial Integro-Differential Equations [PDF]
Journal of Integral Equations and Applications, 1992 The author discusses a method of lines for nonlinear Volterra partial integro-differential equations of parabolic type. In the first step of discretization, a finite difference method is used in the spatial direction to obtain a system of nonlinear stiff Volterra integro- differential equations in time.
J.-P. Kauthen
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Reducing parabolic partial differential equations to canonical form [PDF]
European Journal of Applied Mathematics, 1994 A simple method of reducing a parabolic partial differential equation to canonical form if it has only one term involving second derivatives is the following: find the general solution of the first-order equation obtained by ignoring that term and then seek a solution of the original equation which is a function of one more independent variable ...
J. F. Harper
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An inverse problem for a parabolic partial differential equation
Rocky Mountain Journal of Mathematics, 1983 This is a very interesting problem and the paper seems to me to be a good piece of work. The investigation involves finding the solution u(x,t) and the coefficient a(x) in the boundary-initial value problem \[ (P)u_ t- u_{xx}+a(x)u=0,\quad ...
W. Rundell
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Homogenization of a nonlinear random parabolic partial differential equation [PDF]
Stochastic Processes and their Applications, 2003 The homogenization problem for a semilinear second order parabolic equation with random coefficients \[ \partial _ {t}u^ \varepsilon = \sum ^ {n}_ {i,j=1}\partial _ {x_ {i}}\Bigl (a_ {ij}\Bigl (\frac {x}{\varepsilon }, \xi _ {t/\varepsilon ^ 2}\Bigr )\partial _ {x_ {j}} u^ \varepsilon \Bigr ) + \frac 1{\varepsilon }g\Bigl (\frac {x}{\varepsilon }, \xi ...
É. Pardoux, Andrey L. Piatnitski
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Parabolic and pseudo-parabolic partial differential equations* [PDF]
Journal of the Mathematical Society of Japan, 1969 Tsuan Wu Ting
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