The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation.
Kulish, Vladimir V., Novozhilov, Vasily B. (2003)
Mathematical Problems in Engineering
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Kulish, Vladimir V., Novozhilov, Vasily B. (2003)
Mathematical Problems in Engineering
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Watson, Neil A. (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Jerzy A. Gawinecki, Agnieszka Gawinecka, Jarosław Łazuka, J. Rafa (2013)
Applicationes Mathematicae
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Theories of heat predicting a finite speed of propagation of thermal signals have come into existence during the last 50 years. It is worth emphasizing that in contrast to the classical heat theory, these nonclassical theories involve a hyperbolic type heat equation and are based on experiments exhibiting the actual occurrence of wave-type heat transport (so called second sound). This paper presents a new system of equations describing a nonlocal model of heat propagation with finite...
Christof Eck, Jiří Jarušek (2001)
Mathematica Bohemica
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A short survey of available existence results for dynamic contact problems including heat generation and heat transfer is presented.
Nelson, M. I., Brindley, J., McIntosh, A. C. (2002)
Journal of Applied Mathematics and Decision Sciences
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Daniele Andreucci, Marianne K. Korten (1993)
Revista Matemática Iberoamericana
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The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1 loc (Rn x (0,T)) to (0.1) ut - Δ(u - 1)+ = 0, in D'(Rn x (0,T)), for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection...
Longjie Xie, Xicheng Zhang (2014)
Studia Mathematica
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We construct the heat kernel of the 1/2-order Laplacian perturbed by a first-order gradient term in Hölder spaces and a zero-order potential term in a generalized Kato class, and obtain sharp two-sided estimates as well as a gradient estimate of the heat kernel, where the proof of the lower bound is based on a probabilistic approach.
Kulasiri, Don, Woodhead, Ian (2005)
Mathematical Problems in Engineering
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Sören Bartels, Tomáš Roubíček (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine estimates are derived, and convergence is proved by careful...
Aebischer, Beat (2007)
Mathematical Problems in Engineering
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Cyril Dennis Enyi, Soh Edwin Mukiawa (2022)
Applications of Mathematics
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This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general stability result with minimal condition on the relaxation function is obtained. The system under investigation, to the best of our knowledge, is new and has not been studied before in the literature. What is more interesting is the fact that our result holds without the imposition of the equal speed of wave propagation condition,...
Cohen, Robert D., Brown, Christopher L., Nickols, Carole, Levey, Pauline, Boucher, Barbara J., Greenwald, Stephen E., Wang, Wen (2011)
Computational & Mathematical Methods in Medicine
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