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A result of existence for an original convection-diffusion equation.

Gérard Gagneux, Guy Vallet (2005)


En este artículo se estudia el análisis matemático de una ley de conservación que no es clásica. El modelo describe procesos estatigráficos en Geología y tiene en cuenta una condición de tasa de erosión limitada. En primer lugar se presentan el modelo físico y la formulación matemática (posiblemente nueva). Tras enunciar la definición solución se presentan las herramientas que permiten probar la existencia de soluciones.

An energy analysis of degenerate hyperbolic partial differential equations.

William J. Layton (1984)

Aplikace matematiky

An energy analysis is carried out for the usual semidiscrete Galerkin method for the semilinear equation in the region Ω (E) ( t u t ) t = i , j = 1 ( a i j ( x ) u x i ) x j - a 0 ( x ) u + f ( u ) , subject to the initial and boundary conditions, u = 0 on Ω and u ( x , 0 ) = u 0 . (E) is degenerate at t = 0 and thus, even in the case f 0 , time derivatives of u will blow up as t 0 . Also, in the case where f is locally Lipschitz, solutions of (E) can blow up for t > 0 in finite time. Stability and convergence of the scheme in W 2 , 1 is shown in the linear case without assuming u t t (which can blow up as t 0 is...

Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type

Barbara Szomolay (2003)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction u ¨ = - γ u ˙ + m ( u 2 ) Δ u - δ | u | α u + f , which is known as degenerate if m ( · ) 0 , and non-degenerate if m ( · ) m 0 > 0 . We would like to point out that, to the author’s knowledge, exponential decay for this type of equations has been studied just for the special cases of α . Our aim is to extend the validity of previous results in [5] to α 0 both to the degenerate and non-degenerate cases of m . We extend our results to equations with...

Global existence of strong solutions to the one-dimensional full model for phase transitions in thermoviscoelastic materials

Elisabetta Rocca, Riccarda Rossi (2008)

Applications of Mathematics

This paper is devoted to the analysis of a one-dimensional model for phase transition phenomena in thermoviscoelastic materials. The corresponding parabolic-hyperbolic PDE system features a strongly nonlinear internal energy balance equation, governing the evolution of the absolute temperature ϑ , an evolution equation for the phase change parameter χ , including constraints on the phase variable, and a hyperbolic stress-strain relation for the displacement variable 𝐮 . The main novelty of the model...

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