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Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile
(Elsevier, 2016)
We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up ...
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, ...
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 ...
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 ...
On the finite space blow up of the solutions of the Swift–Hohenberg equation
(SpringerHeidelberg, 2015-09)
The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture by Gazzola and Pavani (Arch Ration Mech Anal 207(2):717–752, ...
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 ...
Sign-changing blowing-up solutions for thecritical nonlinear heat equation
(Scuola Normale Superiore, 2020)
Let Omega be a smooth bounded domain in R-n and denote the regular part of the Green function on Omega with Dirichlet boundary condition by H(x, y). Assume the integer k0 is sufficiently large, q is an element of Omega and ...
Existence And Multiplicity Of Self-similar Solutions For Heat Equations With Nonlinear Boundary Conditions
(SPRINGER HEIDELBERGHEIDELBERG, 2015)
Further Remarks on the Luo-Hou's Ansatz for a Self-similar Solution to the 3D Euler Equations
(2017)
It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, ...
Weak Concentration And Wave Operator For A 3d Coupled Nonlinear Schrödinger System
(American Institute of Physics Inc., 2015)