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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[...]texto impreso
Jiménez Casas, Ángela ; Rodríguez Bernal, Aníbal | American Institute of Mathematical Sciences | 2011We obtain dynamic boundary conditions as a limit of parabolic problems with null flux where the time derivative concentrates near the boundary.texto impreso
Rodríguez Bernal, Aníbal ; Vidal López, Alejandro ; Langa, J.A. ; Robinson, James C. ; Suárez, A. | American Institute of Mathematical Sciences | 2007The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut ? _u = _u ? b(t)up, with p > 1, b(t) > 0, for all t 2 R, limt!1 b(t) = 0. While the pullback asymptotic behaviour for this [...]texto impreso
Rodríguez Bernal, Aníbal ; Vidal López, Alejandro | American Institute of Mathematical Sciences | 2007We give conditions for the existence of a unique positive complete trajectories for non-autonomous reaction-diffusion equations. Also, attraction properties of the unique complete trajectory is obtained in a pullback sense and also forward in ti[...]texto impreso
Explosive instabilities in spatially discrete reaction-diffusion systems are studied. We identify classes of initial data developing singularities in finite time and obtain predictions of the blow-up times, whose accuracy is checked by compariso[...]texto impreso
Casal, Alfonso C. ; Díaz Díaz, Jesús Ildefonso ; Vegas Montaner, José María | American Institute of Mathematical Sciences | 2011We prove that the mere presence of a delayed term is able to connect the initial state u0 on a manifold without boundary (here assumed given as the set ?? where ? is an open bounded set in RN ) with the zero state on it and in a finite time even[...]texto impreso
Hernández Corbato, Luis ; Romero Ruiz del Portal, Francisco | American Institute of Mathematical Sciences | 2015-07We characterize the sequences of fixed point indices {i(f(n) ,p)} n > = 1 of fixed points that are isolated as an invariant set for a continuous map f in the plane. In particular, we prove that the sequence is periodic and i(f(n) ,p) = 0. This[...]texto impreso
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[...]texto impreso
We show existence and uniqueness of global solutions for reaction-diffusion equations with almost-monotonic nonlinear terms in L-q(Omega) for each 1texto impreso
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 [...]texto impreso
Díaz Díaz, Gregorio ; Díaz Díaz, Jesús Ildefonso | American Institute of Mathematical Sciences | 2015-04This paper deals with several qualitative properties of solutions of some stationary equations associated to the Monge-Ampere operator on the set of convex functions which are not necessarily understood in a strict sense. Mainly, we focus our at[...]texto impreso
We extend some previous local energy method to the study the free boundary generated by the solutions of quenching type parabolic problems involving a negative power of the unknown in the equation.texto impreso
Díaz Díaz, Jesús Ildefonso ; Mingazzini, Tomasso ; Ramos del Olmo, Ángel Manuel | American Institute of Mathematical Sciences | 2012We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The ne[...]texto impreso
We study some retention phenomena on the free boundaries associated to some elliptic and parabolic problems of reaction-diffusion type. This is the case, for instance, of the wait in g time phenomenon for solutions of suitable parabolic equation[...]texto impreso
Díaz Díaz, Jesús Ildefonso ; Rakotoson, Jean Michel Theresien | American Institute of Mathematical Sciences | 2010-07We prove the existence of an appropriate function (very weak solution) u in the Lorentz space L(N') (,infinity)(Omega), N' = (N)(N - 1) satisfying Lu - Vu + g (x, u, del u) = mu in Omega an open bounded set of R(N), and u = 0 on partial derivati[...]
