# Search results for: Pablo Groisman

Communications on Pure and Applied Mathematics > 74 > 7 > 1453 - 1492

*n*‐dimensional Euclidean space. These models are designed to capture basic growth features that are expected to manifest at the

*mesoscopic*level for several classical self‐interacting processes originally defined at the

*microscopic scale*. It includes once‐reinforced random walk with strong reinforcement, origin‐excited random...

Journal of Statistical Physics > 2015 > 158 > 6 > 1213-1233

Stochastic Processes and their Applications > 2012 > 122 > 5 > 2185-2210

Journal of Mathematical Analysis and Applications > 2012 > 385 > 1 > 150-166

Journal of Statistical Physics > 2012 > 149 > 4 > 629-642

Computers and Chemical Engineering > 2010 > 34 > 2 > 223-231

Journal of Multivariate Analysis > 2009 > 100 > 5 > 981-992

Physica D: Nonlinear Phenomena > 2009 > 238 > 2 > 209-215

Annali di Matematica Pura ed Applicata ( 01923 -) > 2007 > 186 > 2 > 341-358

*u*‖

^{2}

_{ H }

^{1}

_{(Ω)}

^{2}/‖

*u*‖

^{2}

_{ L }

^{2}

_{(∂Ω)}for functions that vanish in a subset

*A*⊂ Ω, which we call the hole. We look for holes that minimize the best Sobolev trace constant among subsets of Ω with prescribed volume. First, we find a formula for the first variation of...

*u*

_{ t }=Δ

*u*+

*u*

^{ p }with homogeneous Dirichlet boundary conditions has solutions with blow-up if

*p*>1. An adaptive time-step procedure is given to reproduce the asymptotic behavior of the solutions in the numerical approximations. We prove that the numerical methods reproduce the blow-up cases, the blow-up rate and the blow-up time. We also localize the numerical blow-up set.

Journal of Computational and Applied Mathematics > 2001 > 135 > 1 > 135-155

_{t}=u

_{x}

_{x}+u

^{p}in a bounded interval, (0,1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical...