Información del autor
Autor Herrero, Miguel A. |
Documentos disponibles escritos por este autor (100)
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We consider here the radial Stefan problem with Gibbs-Thomson law, which is a classical model describing growth or melting of a spherical crystal in a surrounding liquid. We shall specialize to the cases of two and three space dimensions and dis[...]texto impreso
The paper is a nice brief review of fundamental results about the initial value problem for one-dimensional nonlinear degenerate parabolic equations of "porous media'' type: ut=[?(ux)]x, x?R, t> 0, with ? continuous, nondecreasing, ?(0)=0, |?(s)[...]texto impreso
Velázquez, J.J. L. ; Galaktionov, V. A. ; Posashkov, S. A. ; Herrero, Miguel A. | Pergamon-Elsevier Science | 1993The authors study asymptotic behaviour of positive solutions of equations of the type ut =??(u)±Q(u), where ?? and Q are given positive functions. By determining an auxiliary function F(u) appearing in an expression posed by A. Friedman and B. M[...]texto impreso
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The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p?2 Du)(ptexto impreso
This paper deals with the following initial value problem: (1) ?u/?t??u+u p=0 on RN, N?1, 0 0,u(x,t)> 0}, u(x,t) being the solution of (1). The following results are established. (i) If u0(x)?A(|x|)+B|x?a|2/(1?p) for some a?RN where A(|x|)=o(|x[...]texto impreso
Bellomo , Nicola ; Herrero, Miguel A. ; Tosin, Andrea | American Institute of Mathematical Sciences | 2013-09This paper deals with the modeling of social competition, possibly resulting in the onset of extreme conflicts. More precisely, we discuss models describing the interplay between individual competition for wealth distribution that, when coupled [...]texto impreso
In this work a mathematical model for the interaction of two key signalling molecules in rat tibia ossification is presented and discussed. The molecules under consideration are Indian hedgehog (Ihh) and parathyroid hormone-related peptide (PTHr[...]texto impreso
Herrero, Miguel A. ; Oleaga Apadula, Gerardo Enrique ; Velázquez, J.J. L. | American Mathematical Society | 2006This work deals with the linear wave equation considered in the whole plane R2 except for a rectilinear moving slit, represented by a curve ? (t) = {(x1, 0) : ??texto impreso
We analyse a mathematical model for the growth of thin filaments into a two dimensional medium. More exactly, we focus on a certain reaction/diffusion system, describing the interaction between three chemicals (an activator, an inhibitor and a g[...]texto impreso
The author deals with the propagation of the support of the initial function in the following problem: ut?(um)xx+cun=0 on R×(0,+?), u(x,0)=u0(x) on R with n?m> 1, c> 0; u0 is bounded and has bounded support, and u0?0. The author proves the follo[...]texto impreso
Bénilan, Philippe ; Boccardo, L. ; Herrero, Miguel A. | Libreria Editrice Universitaria Levrotto & Bella | 1989Let f?L1(RN), N?1, f?0, and consider the Cauchy problem ut=?um on ]0,?[×RN, u(0,?)=f on RN. The authors prove that as m??, the corresponding solutions um(t)?u_=f+?w in L1(RN), uniformly for t in a compact set in ]0,?[, where 0?w_?L1(Rn) is the s[...]texto impreso
We consider here the problem of describing the melting of an ice ball surrounded by water. The corresponding mathematical model consists of the Stefan problem with radial symmetry. We obtain asymptotic expansions for the radius of the melting ba[...]texto impreso
In this expository paper the equation (1) ut=div(|?u|m?1 ?u) is discussed in one space dimension (N=1). L?-gradient bounds have been established for arbitrary N by the reviewer and R. Rostamian [Math. Ann. 259 (1982), no. 1, 53–70; Proc. Roy. So[...]texto impreso
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Oleaga Apadula, Gerardo Enrique ; Herrero, Miguel A. ; Velázquez, J.J. L. | Royal Society of London | 2004-02-08Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle psi not equal 0 at their junction, examples can be[...]texto impreso
Herrero, Miguel A. ; Oleaga Apadula, Gerardo Enrique ; Velázquez, J.J. L. | Royal Society of London | 2004Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle psi not equal 0 at their junction, examples can be[...]texto impreso
We consider the problem (1) u(t) = u(xx) + e(u) when x is-an-element-of R, t > 0, (2) u (x, 0) = u0(x) when x is-an-element-of R, where u0(x) is continuous, nonnegative and bounded. Equation (1) appears as a limit case in the analysis of combus[...]texto impreso
Arias, C. ; Herrero, Miguel A. ; Acosta, F. J. ; Fernandez Arias, c. | Nature Publishing Group | 2017Unlike other cell types, T cells do not form spatially arranged tissues, but move independently throughout the body. Accordingly, the number of T cells in the organism does not depend on physical constraints imposed by the shape or size of speci[...]texto impreso
Some propagation properties, including a discussion on the existence of compactly supported solutions and the asymptotics of the interfaces thereby determined, are considered for the Cauchy problem u t =(|u x | m-1 ·u x ) x in S=?×(0,?); u(x,0)=[...]texto impreso
Arias, C. F. ; Bertocchini, F. ; Herrero, Miguel A. ; Oleaga Apadula, Gerardo Enrique | Cambridge University Press | 2020-12-23One of the most remarkable aspects of human homeostasis is bone remodeling. This term denotes the continuous renewal of bone that takes place at a microscopic scale and ensures that our skeleton preserves its full mechanical compliance during ou[...]texto impreso
We analyse the set of nonnegative, global, and radial solutions (radial solutions, for short) of the equation -?u + u(p) = f in R(N), N ? 1, where 0texto impreso
We study in this paper the asymptotic behaviour of solutions of a nonlinear Fokker-Plank equation. Such an equation describes the evolution of radiation for a gas of photons, which interacts with electrons by means of Compton scattering and Brem[...]texto impreso
This book is addressed at curricula in applied mathematics, bio-physics, bio-mathematics, and theoretical biology and medicine. It is proposed as an advanced textbook for graduate interdisciplinary courses having as a common point the interest i[...]texto impreso
In this paper we consider some systems of ordinary differential equations which are related to coagulation-fragmentation processes. In particular, we obtain explicit solutions {c(k)(t)} of such systems which involve certain coefficients obtained[...]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[...]texto impreso
Positive solutions of the semilinear parabolic equations u(t) - u(xx) = u(p), p > 1 and u(t) - u(xx) = e(u) for - ? 0 which blow up at a single point x = 0 at a finite instant of time t = T > 0 are considered. Using formal me[...]texto impreso
We consider nonnegative solutions of the semilinear parabolic equation u t —u xx + u p = 0, -? 0, 0texto impreso
We discuss the existence of travelling-wave solutions with interfaces for the nonlinear heat equation with absorption ut = a(um)xx – bu(n) with a, b> 0 and m, n ? R. Several situations occur depending on the relative strength of the di[...]texto impreso
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We consider the semilinear system (S) ut?uxx+vp=0, vt?vxx+uq=0(?? 0 and q> 0. We seek nonnegative and nontrivial travelling wave solutions to (S): u(x,t)=?(ct?x), v(x,t)=?(ct?x) possessing sharp fronts, i.e., such that ?(?)=?(?)=0 for ???0 and [...]texto impreso
This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, [...]texto impreso
Radiotherapy consists in the delivery of ionizing radiation with curative goals. It represents a major modality for treating solid malignancies in any anatomical site. It requires extremely precise dosimetry and delivery to control the lesion wh[...]texto impreso
A mathematical model for the formation of microaggregates (microthrombi) of fibrin polymers in blood flow is considered. It is assumed that the former are induced by an external source (which may be of inflammatory or tumor nature) located in a [...]texto impreso
Let (u(t, x), v(t, x)) and (uBAR(t, x), vBAR(t, x)) be two nonnegative classical solutions of (S)[GRAPHICS:{ut=?u+vp, p> 0 ; vt=?v+uq, q> 0] in some strip S(T) = (0, T) x R(N), where 0texto impreso
We show the existence of instantaneous shrinking of the support and finite extinction time for a nonlinear parabolic problem (see (P) below) corresponding to a nonlinear diffusion with absorption phenomenon