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A note on a theorem of Jörgens.

Mathematische Zeitschrift

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

RACSAM

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 almost-everywhere solution to a mixed problem for one degenerate linear evolution system.

Siberian Mathematical Journal

An application of the theory of edge Sobolev spaces to weakly hyperbolic operators

Banach Center Publications

An energy analysis of degenerate hyperbolic partial differential equations.

Aplikace matematiky

An energy analysis is carried out for the usual semidiscrete Galerkin method for the semilinear equation in the region$\Omega$ (E) ${\left(t{u}_{t}\right)}_{t}={\sum }_{i,j=1}{\left({a}_{ij}\left(x\right){u}_{{x}_{i}}\right)}_{{x}_{j}}-{a}_{0}\left(x\right)u+f\left(u\right)$, subject to the initial and boundary conditions, $u=0$ on $\partial \Omega$ and $u\left(x,0\right)={u}_{0}$. (E) is degenerate at $t=0$ and thus, even in the case $f\equiv 0$, time derivatives of $u$ will blow up as $t\to 0$. 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 ${u}_{tt}$ (which can blow up as $t\to 0$ is...

Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

Mathematical Modelling of Natural Phenomena

In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev 

Boundary value problems for some classes of degenerating second order partial differential equations.

Memoirs on Differential Equations and Mathematical Physics

${C}^{\infty }$-well posedness of the Cauchy problem for quasi-linear hyperbolic equations with coefficients non-Lipschitz in time and smooth in space

Banach Center Publications

In this paper we prove the ${C}^{\infty }$-well posedness of the Cauchy problem for quasi-linear hyperbolic equations of second order with coefficients non-Lipschitz in t ∈ [0,T] and smooth in x ∈ ℝⁿ.

Decay of solutions of a degenerate hyperbolic equation.

Electronic Journal of Differential Equations (EJDE) [electronic only]

Decay of solutions of some degenerate hyperbolic equations of Kirchhoff type

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the asymptotic behavior of solutions to the damped, nonlinear vibration equation with self-interaction $\stackrel{¨}{u}=-\gamma \stackrel{˙}{u}+{m\left(\parallel \nabla u\parallel }^{2}{\right)\Delta u-\delta |u|}^{\alpha }u+f,$ which is known as degenerate if $m\left(·\right)\ge 0$, and non-degenerate if $m\left(·\right)\ge {m}_{0}>0$. 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 $\alpha$. Our aim is to extend the validity of previous results in  to $\alpha \ge 0$ both to the degenerate and non-degenerate cases of $m$. We extend our results to equations with...

Errata to : “On pseudosymmetric systems with one space variable”

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Bollettino dell'Unione Matematica Italiana

Existence and asymptotic behaviour for a degenerate Kirchhoff -Carrier model with viscosity and nonlinear boundary conditions.

Revista Matemática Complutense

The present paper studies the existence and uniqueness of global solutions and decay rates to a given nonlinear hyperbolic problem.

Existence and boundary stabilization of a nonlinear hyperbolic equation with time-dependent coefficients.

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain.

International Journal of Mathematics and Mathematical Sciences

Existence theory for nonlinear hyperbolic systems in nonconservative form.

Forum mathematicum

Existence, uniqueness and regularity for Kruzkov's solutions of the Burger-Carleman's system

Annales de la Faculté des sciences de Toulouse : Mathématiques

Global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator

Annales Polonici Mathematici

The aim of this paper is to prove the existence of the global attractor of the Cauchy problem for a semilinear degenerate damped hyperbolic equation involving the Grushin operator with a locally Lipschitz nonlinearity satisfying a subcritical growth condition.

Global existence and asymptotic behavior of solutions for a class of nonlinear degenerate wave equations.

Differential Equations &amp; Nonlinear Mechanics

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

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 $\vartheta$, an evolution equation for the phase change parameter $\chi$, 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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