Results 61 to 70 of about 976 (113)
arXiv, 2006 This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann equation. Many open problems and possible directions for future research are discussed.
arxiv
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
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
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
Carleman inequality for a linear degenerate parabolic problem [PDF]
arXiv, 2020 In this work, we prove a Carleman estimate for a parabolic problem which has a dissipative degenerate term. The prove relies on choose a suitable weight function that change of sign inside the control domain.
arxiv
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
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.
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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
Analysis and Geometry in Metric SpacesWe consider degenerate Kolmogorov-Fokker-Planck operators ℒu=∑i,j=1qaij(x,t)uxixj+∑k,j=1Nbjkxkuxj−ut,{\mathcal{ {\mathcal L} }}u=\mathop{\sum }\limits_{i,j=1}^{q}{a}_{ij}\left(x,t){u}_{{x}_{i}{x}_{j}}+\mathop{\sum }\limits_{k,j=1}^{N}{b}_{jk}{x}_{k}{u}_{{
Biagi Stefano, Bramanti Marco
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Ireneo Peral: Forty Years as Mentor
Advanced Nonlinear Studies, 2017 In this article we present a survey of the Ph.D. theses that have been completed under the advice of Ireneo Peral.Following a chronological order, we summarize the main results contained in the works of the former students of Ireneo Peral.
Abdellaoui Boumediene +9 more
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