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This paper deals with the Cauchy problem u(t)-u(xx)+u(p)=0; -infinitytexto impreso
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[...]texto impreso
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 1texto impreso
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[...]texto impreso
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, 0texto impreso
We consider the Cauchy problem u t -u xx +u p =0,x??,t> 0,u(x,0)=u 0 (x),x??, where 0texto impreso
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 [...]texto impreso
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 =[...]texto impreso
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[...]texto impreso
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 = Ttexto impreso
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=Ttexto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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 [...]
