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Autor Herrero, Miguel A. |
Documentos disponibles escritos por este autor (100)
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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[...]