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Autor Herrero, Miguel A. |
Documentos disponibles escritos por este autor (100)
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This paper deals with the Cauchy problem u(t)-u(xx)+u(p)=0; -infinity![]()
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We consider here the homogeneous Dirichlet problem for the equation u(t)= u?u - ?|?u|(2) with ? ? R, u ? 0, in a noncylindrical domain in space-time given by |x| ? R(t) = (T - t)(p), with p > 0. By means of matched asymptotic expansion techniqu[...]![]()
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The authors consider the problem ut?div(|?u|p?2?u)=0 in (0,?)×RN, u(x,0)=u0(x). They show that if N?2 and 1![]()
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This paper examines a system first introduced by Keller and Segel in 1970 to model the tendency of slime molds to move towards higher concentrations of a chemical which they themselves secrete. The paper particularly addresses the question of bl[...]![]()
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In this paper the authors study the asymptotic behaviour of solutions u?(x,t) of the Cauchy problems as ? goes to zero: ut???u+up=0, x?RN, t> 0; u(x,0)=u0(x), x?RN, 0![]()
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We consider the Cauchy problem u t -u xx +u p =0,x??,t> 0,u(x,0)=u 0 (x),x??, where 0![]()
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Cappuccio, Antonio ; Herrero, Miguel A. ; Nuñez, Luis | American Association of Physicists in Medicine | 2009-01In tumor radiosurgery, a high dose of radiation is delivered in a single session. The question then naturally arises of selecting an irradiation strategy of high biological efficiency. In this study, the authors propose a mathematical framework [...]![]()
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Consider the Cauchy problem u(t) - u(xx) - F(u) = 0; x is-an-element-of R, t> 0 u(x, 0) = u0(x); x is-an-element-of R where u0 (x) is continuous, nonnegative and bounded, and F(u) = u(p) with p > 1, or F(u) = e(u). Assume that u blows up at x =[...]![]()
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We consider the following nonlinear system of parabolic equations: (1) ut =?u???(u?v), ?vt =?v+u?av for x?B R, t> 0. Here ?,? and a are positive constants and BR is a ball of radius R> 0 in R2. At the boundary of BR, we impose homogeneous Neuma[...]![]()
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We consider the equation (E) u(t) = ?u + u(p) where x ? R(N) (N ? 1), t > 0, p > 1. We show that if N ? 11 and p > N - 2 (N - 1)1/2/(N - 4) - 2(N - 1)1/2 then there exist radial and positive solutions of (E) which blow up at x = 0, t = T![]()
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Let u be a solution of the Cauchy problem ut=uxx+up, x?R, t> 0, u(x,0)=u0(x), x?R, where p> 1 and u0 is continuous, nonnegative, and bounded. Suppose that u blows up at t=T![]()
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The object of this paper is the study of blowing-up phenomena for the initial-boundary value problem (Pa): ut=uxx+?eu for (x,t)?(0,1)×(0,+?), u(0,t)=asin?t and u(1,t)=0 for t?[0,+?), u(x,0)=u0(x) for x?(0,1), where u0(x) is a continuous and boun[...]![]()
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In this work we succintly review the main features of bone formation in vertebrates. Out of the many aspects of this exceedingly complex process, some particular stages are selected for which mathematical modelling appears as both feasible and d[...]![]()
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We consider the semilinear parabolic system (S) { ut-?u=vp ; vt-?v=uq, where x ? R(N) (N ? 1), t > 0, and p, q are positive real numbers. At t=0, nonnegative, continuous, and bounded initial values (u0(x), v0(x)) are prescribed. The correspon[...]![]()
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This work is concerned with the system (S) {u(t)=Delta u-chi del(u del upsilon) for x is an element of Omega, t> 0 Gamma upsilon(t)=Delta upsilon=Delta upsilon+(u-1) for x is an element of Omega, t> 0 where Gamma; chi are positive constants and [...]![]()
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López Alfonso, Juan Carlos ; Butazzo, Giuseppe ; García Archilla, B. ; Herrero, Miguel A. ; Nuñez, L. | American Institute of Mathematical Sciences | 2012-09Radiotherapy is an important clinical tool to fight malignancies. To do so, a key point consists in selecting a suitable radiation dose that could achieve tumour control without inducing significant damage to surrounding healthy tissues. In spit[...]![]()
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We consider the Cauchy problem (1) ut=uxx+up, 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 here the generic asymptotic be[...]![]()
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In the following the reader will find a short description of some issues related to the modeling, analysis and simulation of large populations of living systems, a research field which is currently deserving a considerable interest, and that has[...]![]()
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Background: The choice of any radiotherapy treatment plan is usually made after the evaluation of a few preliminary isodose distributions obtained from different beam configurations. Despite considerable advances in planning techniques, such fin[...]![]()
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Herrero, Miguel A. ; Oleaga Apadula, Gerardo Enrique ; Echeverri, L.F. ; López, J. M. | Springer | 2014-12This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodelin[...]![]()
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We obtain existence and uniqueness of solutions with compact support for some nonlinear elliptic and parabolic problems including the equations of one-dimensional motion of a non-newtonian fluid. Precise estimates for the support of these soluti[...]![]()
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This note is an account of results obtained by the author [Rev. Real Acad. Cienc. Exact. Fís. Natur. Madrid 75 (1981), no. 5, 1165–1183; MR0649591 (83m:35076)], and the author and J. L. Vázquez ["On a class of nonlinear parabolic equations'', to[...]![]()
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The authors consider the system, defined for t> 0, -?![]()
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The authors consider blow-up for the equation (1) ut=?u+up (x?RN, t> 0), where p> 1 and N> 1. For N> 11and (2) p> (N?2(N?1)1/2)/(N?4?2(N?1)1/2)=p1(N) there exist some radial positive solutions that blow up at x=0, t=T![]()
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A simple model of chemical kinetics with two concentrations u and v can be formulated as a system of two parabolic variational inequalities with reaction rates v(p) and u(q) for te diffusion processes of u and v, respectively. It is shown that i[...]![]()
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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[...]