Uniqueness of Solution of the Unsteady Filtration Problem in Heterogeneous Porous Media [PDF]
arXiv, 2015 We establish uniqueness of the solution of the unsteady state dam problem in the heterogeneous and rectangular case assuming the dam wet at the bottom and dry near to the top.
arxiv
Smooth counterexamples to strong unique continuation for a Beltrami system in $\mathbb{C}^2$ [PDF]
arXiv, 2011 We construct an example of a smooth map $\mathbb{C}\to\mathbb{C}^2$ which vanishes to infinite order at the origin, and such that the ratio of the norm of the $\bar z$ derivative to the norm of the $z$ derivative also vanishes to infinite order. This gives a counterexample to strong unique continuation for a vector valued analogue of the Beltrami ...
arxiv
On the Cauchy problem for a general fractional porous medium equation with variable density [PDF]
arXiv, 2013 We study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according with the behavior of the density at infinity.
arxiv
On a fractional sublinear elliptic equation with a variable coefficient [PDF]
arXiv, 2013 We study existence and uniqueness of bounded solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of solutions to an associated fractional porous medium equation with ...
arxiv
Chromatin Landscape Dynamics in the Early Development of the Plant Parasitic Nematode Meloidogyne incognita. [PDF]
Front Cell Dev Biol, 2021 Hassanaly-Goulamhoussen R +9 more
europepmc +1 more source
Local Well-Posedness for Relaxational Fluid Vesicle Dynamics [PDF]
J. Evol. Equ. 18 (4), 1787-1818, 2018, 2015 We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument. Our approach is based on the maximal $L_p$-regularity of the model's linearization.
arxiv
Genome Expression Dynamics Reveal the Parasitism Regulatory Landscape of the Root-Knot Nematode Meloidogyne incognita and a Promoter Motif Associated with Effector Genes. [PDF]
Genes (Basel), 2021 Da Rocha M +10 more
europepmc +1 more source
Mean curvature flow with driving force on fixed extreme points [PDF]
arXiv, 2017 In this paper, we consider the mean curvature flow with driving force on fixed extreme points in the plane. We give a general local existence and uniqueness result of this problem with $C^2$ initial curve. For a special family of initial curves, we classify the solutions into three categories.
arxiv
Measurable process selection theorem and non-autonomous inclusions [PDF]
arXiv, 2017 A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow solutions to blow up in finite time and then obtain local semi-processes.
arxiv
The gyrokinetic limit for the Vlasov-Poisson system with a point charge [PDF]
arXiv, 2017 We consider the asymptotics of large external magnetic field for a 2D Vlasov-Poisson system governing the evolution of a bounded density interacting with a point charge. In a suitable asymptotical regime, we show that the solution converges to a measure-valued solution of the Euler equation with a defect measure.
arxiv