© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.Although macrophages are part of the human immune system, it has been remarkably observed in laboratory experiments that decreasing its number can slow down the ...

For a class of drift–diffusion systems Kurokiba et al. [M. Kurokiba, T. Nagai, T. Ogawa, The uniform boundedness and threshold for the global existence of the radial solution to a drift–diffusion system, Commun. Pure ...

We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S-2, u(t) = Delta u + vertical bar del u vertical bar(2)u in Omega x (0, T) u = phi on partial derivative Omega x (0, ...

In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as ...

Let Omega be a smooth bounded domain in R-n, n >= 5. We consider the classical semilinear heat equation at the critical Sobolev exponent. ut =Delta u + un+2/n-2 in Omega x (0, infinity), u = 0 on partial derivative Omega ...

In this paper we construct solutions which develop two negative spikes as epsilon -> 0(+) for the problem -Delta u = vertical bar u vertical bar(4/(N-2)) u + epsilon f(x) in Omega, u = 0 on partial derivative Omega, where ...

© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S2, ut=Δu+|∇u|2uinΩ×(0,T)u=φon∂Ω×(0,T)u(·,0)=u0inΩ,where Ω is ...

We consider the Cauchy problem for the energy critical heat equation {ut=Δu+|u|4n−2uinRn×(0,T)u(⋅,0)=u0inRn in dimension n = 5. More precisely we find that for given points q 1 ,q 2 ,..,q k and any sufficiently small T ...

We exhibit a new concentration phenomenon for the supercritical problem -Delta v = lambda v + vertical bar v vertical bar(p-2) v in Omega, v = 0 on partial derivative Omega, as p -> 2*(N,m) from below, where 2*(N, m) := 2 ...