Mayte Pérez-Llanos

Critical exponents for a semilinear parabolic equation with variable reaction

In this paper we study the blow-up phenomenon for nonnegative solutions to the following parabolic problem: ut(x, t) = ∆u(x, t) + (u(x, t)) , in Ω× (0, T ), where 0 1. When Ω = R we show that if p− > 1 + 2/N then there are global nontrivial solutions while if 1 < p− ≤ p+ ≤ 1+2/N then all solutions to the problem blow up in finite time. Moreover, in case p− < 1+2/N < p+ there are functions p(x) such that all solutions blow up in finite time and functions p(x) such that the problem possesses global nontrivial solutions. When Ω is a bounded domain we prove that there are functions p(x) and domains Ω such that all solutions to the problem blow up in finite time. On the other hand, if Ω is small enough then the problem possesses global nontrivial solutions regardless the size of p(x).

Models for growth of heterogeneous sandpiles via Mosco convergence

In this paper we study the asymptotic behavior of several classes of power-law functionals involving variable expo- nents pn(·) →∞ , via Mosco convergence. In the particular case pn(·) = np(·), we show that the sequence {Hn} of functionals Hn : L 2 (R N ) → (0, +∞ )g iven by Hn(u) = � � RN λ(x) n np(x) � ∇u(x) � np(x) dx if u ∈ L 2 � R N � ∩ W 1,np(·) � R N � ,

Numerical Approximations for a Nonlocal Evolution Equation

In this paper we study numerical approximations of continuous solutions to the nonlocal

AN ANISOTROPIC INFINITY LAPLACIAN OBTAINED AS THE LIMIT OF THE ANISOTROPIC (p, q)-LAPLACIAN

p

Anisotropic Variable Exponent (p(·), q(·))-Laplacian with Large Exponents

-Laplacian type diffusion equation,

The sublinear problem for the 1 -homogeneous p -Laplacian

u_t (t,x) = \int_{\Omega} J(x-y)|u(t,y) - u(t,x)|^{p-2}(u(t,y) - u(t,x)) \, dy

Opinion Formation Models with Heterogeneous Persuasion and Zealotry

. First, we find that a semidiscretization in space of this problem gives rise to an ODE system whose solutions converge uniformly to the continuous one as the mesh size goes to zero. Moreover, the semidiscrete approximation shares some properties of the continuous problem: it preserves the total mass and the solution converges to the mean value of the initial condition as

Inhomogeneous torsional creep problems in anisotropic Orlicz Sobolev spaces

t

A Nonlocal Operator Breaking the Keller–Osserman Condition

goes to infinity. Next, we also discretize the time variable and present a totally discrete method which also enjoys the above mentioned properties. In addition, we investigate the limit as

A NONLOCAL 1-LAPLACIAN PROBLEM AND MEDIAN VALUES

p