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Chaos for the Hyperbolic Bioheat Equation [PDF]
Discrete and Continuous Dynamical Systems, 2015 The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that
J Alberto Conejero +2 more
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Dunkl Hyperbolic Equations [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
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Hyperbolic integrodifferential equations [PDF]
Proceedings of the American Mathematical Society, 1975 Hyperbolic integrodifferential equations are defined and conditions sufficient for hyperbolicity are given. The theory includes that of constant coefficient hyperbolic partial differential equations. Other examples are given.
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On the Parabolic and Hyperbolic Liouville Equations [PDF]
Communications in Mathematical Physics, 2021 AbstractWe study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $$\lambda \beta e^{\beta u }$$ λ β e β
Oh, Tadahiro +2 more
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Weak Solutions for a Simple Hyperbolic System [PDF]
, 2001 The model studied concerns a simple first-order hyperbolic system. The solutions in which one is most interested have discontinuities which persist for all time, and therefore need to be interpreted as weak solutions.
Lyne, Owen D., Williams, David S.
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Hyperbolic Methods for Einstein’s Equations [PDF]
Living Reviews in Relativity, 1998 Je passe en revue les aspects évolutifs de la relativité générale, en particulier ceux liés au caractère hyperbolique des équations de champ et aux applications ou conséquences que cette propriété entraîne. J'examine plusieurs approches pour obtenir des systèmes d'équations hyperboliques symétriques à partir des équations d'Einstein en supprimant ...
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Exact and Fast Numerical Algorithms for the Stochastic Wave Equation [PDF]
, 2003 On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions.
Martin, A. +9 more
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Lack of controllability of the heat equation with memory [PDF]
, 2012 We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero ...
Andrei Halanay, Pandolfi, Luciano
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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Solution method for the time-fractional hyperbolic heat equation [PDF]
, 2021 In this article, we propose a method to solve the time-fractional hyperbolic heat equation. We first formulate a boundary value problem for the standard hyperbolic heat equation in a finite domain and provide an analytical solution by means of separation
Font Martínez, Francesc
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