Results 81 to 90 of about 1,990 (139)
Selfsimilar Equivalence of Porous Medium and p-Laplacian Flows [PDF]
arXiv, 2007 We demonstrate the equivalence between the two popular models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. The equivalence is shown at the level of selfsimilar solutions.
arxiv
A non-standard evolution problem arising in population genetics
, 2009 We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries, supplemented by a ...
Chalub, Fabio A. C. C., Souza, Max O.
core +1 more source
Proteus mirabilis swarm-colony development with drift [PDF]
arXiv, 2008 We prove a global existence result for a model describing the swarming phenomenon of the bacterium Proteus mirabilis. The model consists of an ordinary differential equation coupled with an age-structured equation involving nonlinear degenerate diffusion and an additional drift term.
arxiv
Boundary Value Problems, 2013 The aim of this paper is to study the extinction of solutions of the initial boundary value problem for ut=div(|∇u|p(x,t)−2∇u)+b(x,t)|u|q−a0u. The authors discuss how the relations of p(x,t) and dimension N affect the properties of extinction in finite ...
Peng Sun, Mingji Liu, C. Cao
semanticscholar +1 more source
Well-posedness of a porous medium flow with fractional pressure in Sobolev spaces
, 2016 The nonnegative solution for a linear degenerate diffusion transport eqution is proved. As a result, we show the existence and uniqueness of the solution for the fractional porous medium equation in Sobolev spaces $H^\alpha$ with nonnegative initial data,
Xiao, Weiliang, Zhou, Xuhuan
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Existence of solutions for degenerate parabolic equations with singular terms
, 2015 In this paper we deal with parabolic problems whose simplest model is $$ \begin{cases} u'- \Delta_{p} u + B\frac{|\nabla u|^p}{u} = 0 & \text{in} (0,T) \times \Omega,\newline u(0,x)= u_0 (x) &\text{in}\ \Omega, \newline u(t,x)=0 &\text{on}\ (0,T ...
Dall'Aglio, Andrea +2 more
core +1 more source
Uniqueness for solutions of the two-phase Stefan problem with signed measures as data [PDF]
arXiv, 2008 We show uniqueness of solutions to the two-phase Stefan problem which have signed measures as initial data.
arxiv
Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves [PDF]
arXiv, 2009 Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different techniques.
arxiv
Interior Estimates for Generalized Forchheimer Flows of Slightly Compressible Fluids
Advanced Nonlinear Studies, 2017 The generalized Forchheimer flows are studied for slightly compressible fluids in porous media with time-dependent Dirichlet boundary data for the pressure. No restrictions are imposed on the degree of the Forchheimer polynomial. We derive, for all time,
Hoang Luan T., Kieu Thinh T.
doaj +1 more source
Inverse coefficient problem for Grushin-type parabolic operators
, 2013 The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators studied in this paper.
Beauchard, Karine, Cannarsa, Piermarco
core +1 more source