Results 21 to 30 of about 6,537 (288)
Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations [PDF]
The Scientific World Journal, 2016 This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0)=0) and advection-degenerate (at h′(0)=0) reaction-diffusion-advection (RDA) equation.
Faustino Sánchez-Garduño +1 more
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A Non-degenerate Scattering Theory for the Wave Equation on Extremal Reissner–Nordström [PDF]
Communications in Mathematical Physics, 2020 AbstractIt is known that sub-extremal black hole backgrounds do not admit a (bijective) non-degenerate scattering theory in the exterior region due to the fact that the redshift effect at the event horizon acts as an unstable blueshift mechanism in the backwards direction in time. In the extremal case, however, the redshift effect degenerates and hence
Angelopoulos, Yannis +2 more
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Advances in Nonlinear Analysis, 2022 This article deals with the degenerate fractional Kirchhoff wave equation with structural damping or strong damping. The well-posedness and the existence of global attractor in the natural energy space by virtue of the Faedo-Galerkin method and energy ...
Yang Wenhua, Zhou Jun
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Exact controllability for degenerate and singular wave equations
Electronic Journal of Differential EquationsIn this article, we study exact controllability for degenerate and singular wave equations with a general coefficient. We estimate the observability inequality by the multiplier method and determine the observability time. We also deduce the exact controllability of the corresponding degenerate and singular control problem at a sufficiently large ...
Guang Zhang, Shugen Chai
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Linear stabilization for a degenerate wave equation in non divergence form with drift [PDF]
Bulletin of Mathematical SciencesWe consider a degenerate wave equation in one dimension, with drift and in presence of a leading operator which is not in divergence form. We impose a homogeneous Dirichlet boundary condition where the degeneracy occurs and a boundary damping at the ...
Genni Fragnelli, Dimitri Mugnai
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Travelling wave solutions for doubly degenerate reaction-diffusion equations [PDF]
ANZIAM Journal, 2010 AbstractThis paper concerns a nonlinear doubly degenerate reaction–diffusion equation which appears in a bacterial growth model and is also of considerable mathematical interest. A travelling wave analysis for the equation is carried out. In particular, the qualitative behaviour of both sharp and smooth travelling wave solutions is analysed.
M. B. A. MANSOUR +1 more
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Travelling wave phenomena in non-linear diffusion degenerate Nagumo equations [PDF]
Journal of Mathematical Biology, 1997 The authors study the existence of weak travelling wave solutions \(u(x,t)= \phi(x- at)\) for the equation \[ u_t= [D(u)u_x]_x+ g(u),\quad (x,t)\in\mathbb{R}\times \mathbb{R}_+,\tag{1} \] where, for a given \(\alpha\in(0, 1)\), the function \(D\) and \(g\), defined on the interval \([0,1]\), satisfy the conditions: 1) \(g(0)= g(\alpha)= g(1)= 0\), \(g ...
Sánchez-Garduño, F, Maini, P
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On exact solutions of a degenerate quasilinear wave equation with source term
Electronic Journal of Differential Equations, 2006 In this paper, we construct exact solutions of the Cauchy problem of degenerate quasilinear wave equation of Kirchhoff type, and study the effect of the nonlinear terms on the existence of solutions.
Nour-Eddine Amroun, Abbes Benaissa
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Decay of solutions of a degenerate hyperbolic equation
Electronic Journal of Differential Equations, 1998 This article studies the asymptotic behavior of solutions to the damped, non-linear wave equation $$ ddot u +gamma dot u -m(|abla u|^2)Delta u = f(x,t),, $$ which is known as degenerate if the greatest lower bound for $m$ is zero, and non-degenerate if ...
Julio G. Dix
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Traveling Waves in Degenerate Diffusion Equations
Communications in Mathematical Research, 2023 Summary: In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited ...
Xu, Tianyuan, Yin, Jingxue
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