Related papers: Morse indices of multiple blow-up solutions to the…

We are concerned with the Sinh-Gordon equation in bounded domains. We construct blow up solutions with residual mass exhibiting either partial or asymmetric blow up, i.e. where both the positive and negative part of the solution blow up.…

We study the existence of large solutions for nonlocal Dirichlet problems posed on a bounded, smooth domain, associated to fully nonlinear elliptic equations of order $2s$, with $s\in (1/2,1)$, and a coercive gradient term with subcritical…

This paper investigates the connection between blow-up solutions of scalar reaction-diffusion equations, in particular of $u_t = u_{xx} + u^2, $ and its counterpart - eternally existing solutions like heteroclinic orbits - by complex time.…

For the Schr\"odinger map problem from 2+1 dimensions into the 2-sphere we prove the existence of equivariant finite time blow up solutions that are close to a dynamically rescaled lowest energy harmonic map, the scaling parameter being…

We study blowup solutions of the 6D energy critical heat equation $u_t=\Delta u+|u|^{p-1}u$ in $\R^n\times(0,T)$. A goal of this paper is to show the existence of type II blowup solutions predicted by Filippas, Herrero and Vel\'azquez…

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove…

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically…

We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\mathbb R^d\to S^d$. For each dimension $d>2+k(2+2\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched…

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…

We give a compactness result for Brezis-Merle Problem with holderian condition. We look to the case of one or two blow-up points.

We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to which blow-up at the origin and whose local mass at the…

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…

We consider the classical problem of the blowing-up of solutions of the nonlinear heat equation. We show that there exist infinitely many profiles around the blow-up point, and for each integer $k$, we construct a set of codimension $2k$ in…

We consider a non-local Liouville equation corresponding to the prescription of the geodesic curvature on the circle. We build a family of solutions which blow up at a critical point of the harmonic extension of the prescribed curvature…

Consider a compact Riemannian surface $(M,g)$ with nonempty boundary and negative Euler characteristic. Given two smooth non-constant functions $f$ in $M$ and $h$ in $\partial M$ with $\max f= \max h= 0$, under a suitable condition on the…

We consider the slightly subcritical elliptic problem with Hardy term $$ \left\{ \begin{aligned} -\Delta u-\mu\frac{u}{|x|^2} &= |u|^{2^{\ast}-2-\epsilon}u &&\quad \text{in } \Omega\subset\mathbb{R}^N, \\\ u &= 0&&\quad \text{on } \partial…

This note is devoted to a simple proof of blowup of solutions for a nonlinear heat equation. The criterion for a blowup is expressed in terms of a Morrey space norm and is in a sense complementary to conditions guaranteeing the global in…

We construct a solution to a complex nonlinear heat equation which blows up in finite time $T$ only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite…

Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain the two-point Green's function of the relativistic Dirac-Morse problem. This is accomplished by setting up the…

In this article we are concerned with the existence of blow-up solutions to the following boundary value problem $$-\Delta v= \lambda V(x) |x|^2e^v\;\mbox{in}\quad B_1,\quad v=0 \;\mbox{ on }\quad \partial B_1,$$ where $B_1$ is the unit…