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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[...]![]()
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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)[...]![]()
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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[...]![]()
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The authors study the Cauchy problem for the degenerate parabolic equation ut = div(|Du| p?2 Du)(p![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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) : ??![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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)=[...]![]()
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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[...]![]()
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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 0![]()
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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[...]![]()
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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[...]![]()
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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[...]