Información del autor
Autor Herrero, Miguel A. |
Documentos disponibles escritos por este autor (100)
Añadir el resultado a su cesta Hacer una sugerencia Refinar búsqueda
texto impreso
This work is concerned with the following system: [GRAPHICS] which is a model to describe several phenomena in which aggregation plays a crucial role as, for instance, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters.[...]texto impreso
Consider the system (S) {ut–?u=v(p),inQ={(t,x),t> 0, x??}, vt–?v=u(q), inQ, u(0,x)=u0(x)v(0,x)=v0(x)in?, u(t,x)=v(t,x)=0, whent?0, x???, where ? is a bounded open domain in ?N with smooth boundary, p and q are positive parameters, and functions[...]texto impreso
It is well-known that solutions to the one-dimensional supercooled Stefan problem (SSP) may exhibit blow-up in finite time. If we consider (SSP) in a half-line with zero flux conditions at t = 0, blow-up occurs if there exists Ttexto impreso
The authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time. Such a finite-time blow-up of solutions implies chemotactic collapse, na[...]texto impreso
This work is concerned with a reaction-diffusion system that has been proposed as a model to describe acid-mediated cancer invasion. More precisely, we consider the properties of travelling waves that can be supported by such a system, and show [...]texto impreso
We consider an infinite system of reaction-diffusion equations which describes the dynamics of cluster growth, and show that there are solutions which exist for all times and exhibit a sol-gel transition in a finite time. The manner in which suc[...]texto impreso
The authors describe the asymptotic behavior of blow-up for the semilinear heat equation ut=uxx+f(u) in R×(0,T), with initial data u0(x)> 0 in R, where f(u)=up, p> 1, or f(u)=eu. A complete description of the types of blow-up patterns and of the[...]texto impreso
Under Boussinesq and hydraulic engineering approximations, convection in a closed loop under a given external heat flux is governed by an initial-boundary value problem for a first-order nonlinear PDE and an integral equation in two unknown func[...]texto impreso
The paper surveys some recent results for the one-dimensional nonlinear heat equation with absorption subject to continuous nonnegative initial data with compact support. Without absorption, the equation becomes the porous media equation. (Gener[...]texto impreso
This paper deals with the Cauchy problem for the nonlinear diffusion equation ?u/?t - ? (u|u|m+1) = 0 on (0, ?) x RN,u(0, .) = u0 when 0texto impreso
It is well known that the ice-water phase transition can be modelled by the following set of equations: ?T ?t =?Tfor x?R N ??(t),t> 0, (1) T=0for x???(t),t> 0, (2) vn =??T ?n for x???(t),t> 0, (3) where T(x,t) stands for the te[...]texto impreso
Arias, Clemente F. ; Herrero, Miguel A. ; Cuesta, José A. ; Acosta Salmerón, Francisco Javier ; Fernández Arias, Cristina | Royal Society (London) | 2015-07-01Adaptive immune responses depend on the capacity of T cells to target specific antigens. As similar antigens can be expressed by pathogens and host cells, the question naturally arises of how can T cells discriminate friends from foes. In this w[...]texto impreso
This chapter provides a description of some of the mathematical approaches that have been developed to account for quantitative and qualitative aspects of chemotaxis. This last is an important biological property, consisting in motion of cells i[...]texto impreso
In this paper we consider the limit m?+? of solutions of the porous-medium equation ut = ?•(um?u)(x?RN), with N > 1. We conjecture that, for initial data with a unique maximum, the evolution is characterized by the onset of a ‘mesa’ region, in [...]texto impreso
We consider the equation ut=(Um)xx-?un with m> 1, ?> 0, n?m as a model for heat diffusion with absorption. Hence we assume that u?0 for x?R, t?0. We study the regularity of the solution to the Cauchy problem for this degenerate parabolic equatio[...]