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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[...]