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Autor Herrero, Miguel A. |
Documentos disponibles escritos por este autor (100)
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Consider the initial-boundary value problem for ut=?u-?u(q) with ?> 0, 0![]()
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We consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x[...]![]()
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Human societies are formed by different socio-economical classes which are characterized by their contribution to, and their share of, the common wealth available. Cheaters, defined as those individuals that do not contribute to the common wealt[...]![]()
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We consider the following system: [GRAPHICS] which has been used as a model for various phenomena, including motion of species by chemotaxis and equilibrium of self-attracting clusters. We show that, in space dimension N = 3, (S) possess radial [...]![]()
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Consider the Cauchy problem ut=uxx+up, x?R, t> 0, u(x,0)=u0(x), x?R, where p> 1 and u0(x) is continuous, nonnegative and bounded. Assume that u(x,t) blows up at x=0, t=T and set u(x,t)=(T?t)?1/(p?1)?(y,?), y=x/T?t?????, ?=?ln(T?t). Here we show [...]![]()
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Bru Espino, Antonio ; Casero Díaz-Cano, David ; De Franciscis, Sebastiano ; Herrero, Miguel A. | Pergamon-Elsevier Science Ltd | 2008-03Tumour growth can be described in terms of mathematical models from different points of view due to its multiscale nature. Dynamic scaling is a heuristic discipline that exploits the geometrical features of growing fronts using different concept[...]![]()
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Bellomo, Nicola ; Bellouquid, Abdelghani ; Herrero, Miguel A. | Pergamon-Elsevier Science Ltd | 2007-02This paper presents an asymptotic theory for a large class of Boltzmann-type equations suitable to model the evolution of multicellular systems in biology. The mathematical approach described herein shows how various types of diffusion phenomena[...]![]()
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We shall briefly review some early nucleation models, and then examine some aspects of the subsequent evolution of their solutions. Such situation is characterised by the onset of comparatively large clusters that can diffuse into the medium and[...]![]()
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This work is concerned with a model which has been proposed to describe the growth of solid tumors. More precisely, the model under consideration provides a procedure to extract information about the growth dynamics from the analysis of the geom[...]![]()
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This paper concerns the Cauchy problem ut?uxx=up, x?R, t> 0, u(x,0)=u0(x), x?R, where p> 1 and u0(x) is a continuous, nonnegative and bounded function. It has been previously proved that if x=x¯, t=T is a blow-up point, then there are three case[...]![]()
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We consider the Cauchy problem (1) u(t) = u(xx) + u(p); x ? R, t > 0, p > 1 (2) u(x, 0) = u0 (x), x ? R, where u0(x) is continuous, nonnegative and bounded. Assume that the solution u(x, t) of (1), (2) blows up at x = 0, t = T. We describe her[...]![]()
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The pair of parabolic equations u(t) = a ? u + f(u,v), (1) v(t) = b ? b - f(u, v), (2) with a > 0 and b > 0 models the temperature and concentration for an exothermic chemical reaction for which just one species controls the reaction rate f. [...]![]()
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We shall recall some reaction-difussion models which have been used to describe the growth of net-like structures, mainly in a biological context. In particular, a modified activator-inhibitor system proposed by Hans Meinhardt in 1976 will be co[...]![]()
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The authors consider the initial-boundary value problem for the porous medium equation ut =(um)xx in (0,?)×(0,T), where m> 1, 0![]()
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Arias, Clemente F. ; Herrero, Miguel A. ; Acosta Salmerón, Francisco Javier ; Fernández Arias, Clemente | Elsevier | 2014-05-21We formulate and analyze an algorithm of cell fate decision that describes the way in which division vs. apoptosis choices are made by individual T cells during an infection. Such model involves a minimal number of known biochemical mechanisms: [...]![]()
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Fasano, A. ; Herrero, Miguel A. ; López, J. M. ; Medina Reus, Elena | Italian Society for Applied and Industrial Mathematics (SIMAI) | 2010A mathematical model to describe the process of formation of bone tissue by replacement of cartilage tissue is presented and discussed. This model is based on an absorption-diffusion system which describes the interaction of two key signalling m[...]![]()
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Guria, G. T. ; Herrero, Miguel A. ; Zlobina, K. E. | American Institute of Mathematical Sciences | 2009-09In this work a mathematical model for blood coagulation induced by an activator source is presented. Blood coagulation is viewed as a process resulting in fibrin polymerization, which is considered as the first step towards thrombi formation. We[...]![]()
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We briefly review some classical models of aggregate formation with regard to their elementary monomeric components. Particular attention is paid to the role played by explicit solutions in the overall evolution of the theory, for which some rel[...]![]()
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This article considers a mathematical model for tumour growth based on an acid-mediated hypothesis, i.e. the assumption that tumour progression is facilitated by acidification of the region around the tumour-host interface. The resulting destruc[...]![]()
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In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel m[...]![]()
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This work is concerned with some aspects of the social life of the amoebae Dictyostelium discoideum (Dd). In particular, we shall focus on the early stages of the starvation-induced aggregation of Dd cells. Under such circumstances, amoebae are [...]![]()
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Arias, Clemente F. ; Herrero, Miguel A. ; Stern, Claudio D. ; Bertocchini, Federica | Nature Publishing Group | 2017The first obvious sign of bilateral symmetry in mammalian and avian embryos is the appearance of the primitive streak in the future posterior region of a radially symmetric disc. The primitive streak marks the midline of the future embryo. The m[...]![]()
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From the introduction: "We continue here the investigation initiated earlier by us [Trans. Amer. Math. Soc. 314 (1989), no. 1, 187–224] concerning the solvability of the Cauchy problem and the existence of initial traces for nonnegative weak sol[...]![]()
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The initial value problem for the equation (?2 / ?t2 ? ?2 / ?x2) ?T / ?t = (? ?2 / ?t ? ?2 / ?x2) eT, ?> 1, is considered. It is proved that under some restrictions on the initial data there is a curve, denoted by t=??(x), which is positive, [...]![]()
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We consider an infinite system of reaction-diffusion equations that models aggregation of particles. Under suitable assumptions on the diffusion coefficients and aggregation rates, we show that this system can be reduced to a scalar equation, fo[...]