Uniform in discretization error estimates for convection dominated convection-diffusion problems
Uniformly Convergent Difference Schemes for Singularly Perturbed Parabolic Diffusion-Convection Problems Without Turning Points.
Uniqueness and stability of regional blow-up in a porous-medium equation
Uniqueness and stability properties of monostable pulsating fronts
We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular,...
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.
Uniqueness of Monotone Mono-stable Waves for Reaction-Diffusion Equations with Time Delay
Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some competition systems. However, the problem on the uniqueness of traveling wave (for a fixed wave speed)...
Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.
En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3).De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.
Universal bounds for global solutions of a diffusion equation with a mixed local-nonlocal reaction term.
Upper and lower bounds for a reactive-diffuse system with Arrhenius kinetics.
Upper Hausdorff dimension estimates for invariant sets of evolutionary systems on Hilbert manifolds
We prove a generalization of the Douady-Oesterlé theorem on the upper bound of the Hausdorff dimension of an invariant set of a smooth map on an infinite dimensional manifold. It is assumed that the linearization of this map is a noncompact linear operator. A similar estimate is given for the Hausdorff dimension of an invariant set of a dynamical system generated by a differential equation on a Hilbert manifold.
Upper semicontinuity of random attractors for non-compact random dynamical systems.
Upper semicontinuity of the attractor for lattice dynamical systems of partly dissipative reaction diffusion systems.
Variational problems with free boundaries for the fractional Laplacian
We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.
Viral infection model with diffusion and state-dependent delay: a case of logistic growth
We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...
Wave bifurcation in models for heterogeneous catalysis.
Wave of Chaos and Pattern Formation in Spatial Predator-Prey Systems with Holling Type IV Predator Response
The challenges to live in the open water and the diversity of habitats in the marine environments prompts phytoplankton to devise strategies which often involve production of toxins by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor. The functional response of the predator is described by Holling type IV. We investigate wave phenomena and non-linear non-equilibrium pattern formation in a phytoplankton-zooplankton system with Holling type IV functional response....
Waves of Autocrine Signaling in Patterned Epithelia
A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...
Waves of excitations in heterogeneous annular region, asymmetric arrangement
This paper deals with the propagation of waves around a circular obstacle. The medium is heterogeneous: the velocity is smaller in the inner region and greater in the outer region. The interface separating the two regions is also circular, and the obstacle is located eccentrically inside it. The different front portraits are classified.
Weak- solutions for a model of self-gravitating particles with an external potential
The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.
Weak periodic solutions of some quasilinear parabolic equations with data measures.