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A simultaneous blow-up problem arising in tumor modeling
(Springer Verlag, 2019)
© 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 ...
Threshold condition for global existence and blow-up to a radially symmetric drift–diffusion system
(Elsevier, 2012)
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 ...
Singularity formation for the two-dimensional harmonic map flow into S-2
(Springer, 2020)
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, ...
Positive solutions for systems of quasilinear equations with non-homogeneous operators and weights
(Walter de Gruyter, 2020)
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 ...
Green's function and infinite-time bubbling in the critical nonlinear heat equation
(European Mathematical Society, 2020)
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 ...
Double-spike solutions for a critical inhomogeneous elliptic problem in domains with small holes
(ROYAL SOC EDINBURGH, 2008)
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 ...
Singularity formation for the two-dimensional harmonic map flow into S2
(Springer New York LLC, 2020)
© 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 ...
Type II Blow-up in the 5-dimensional Energy Critical Heat Equation
(Springer Verlag, 2019)
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 ...
Concentration with a single sign-changing layer at the higher critical exponents
(Walter de Gruyter GMBH, 2018)
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 ...