On the parabolic gluing method and singularity formation

Asymptotic behavior of solutions to PDEs (35B40) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Singularity in context of PDEs (35A21) Semilinear parabolic equations (35K58)

Cites Work

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Nonradial type II blow-up for the energy-supercritical semilinear heat equation
Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions
On De Giorgi's conjecture in dimension \(N\geq 9\)
Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\)
Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
Slow blow-up solutions for the \(H^1(\mathbb R^3)\) critical focusing semilinear wave equation
On a variational problem with lack of compactness: The topological effect of the critical points at infinity
Two-bubble solutions in the super-critical Bahri-Coron's problem
Type II blow-up mechanisms in a semilinear heat equation with critical Joseph-Lundgren exponent
Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents
Type II blow-up for the four dimensional energy critical semi linear heat equation
Grow up and slow decay in the critical Sobolev case
A type II blowup for the six dimensional energy critical heat equation
Travelling helices and the vortex filament conjecture in the incompressible Euler equations
On the stability of blowup solutions for the critical corotational wave-map problem
Geometry driven type II higher dimensional blow-up for the critical heat equation
Singularity formation for the two-dimensional harmonic map flow into \(S^2\)
Gluing methods for vortex dynamics in Euler flows
Infinite-time blow-up for the 3-dimensional energy-critical heat equation
Green's function and infinite-time bubbling in the critical nonlinear heat equation
A higher speed type II blowup for the five dimensional energy critical heat equation
Type II finite time blow-up for the energy critical heat equation in \(\mathbb{R}^4\)
Type II blow-up in the 5-dimensional energy critical heat equation
Infinite time blow-up for the fractional heat equation with critical exponent
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
Renormalization and blow up for charge one equivariant critical wave maps
Quasilinear Dirichlet problems driven by positive sources
Bubble towers in the ancient solution of energy-critical heat equation
Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
On blow-up rate for sign-changing solutions in a convex domain
Concentration on curves for nonlinear Schrödinger Equations
Seminlinear parabolic equation on bounded domain with critical Sobolev exponent
On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
On Nonexistence of type II blowup for a supercritical nonlinear heat equation
Blow up rate for semilinear heat equations with subcritical nonlinearity
Stable Blowup Dynamics for the 1‐Corotational Energy Critical Harmonic Heat Flow
Infinite time blow-up for half-harmonic map flow from R into S1
Sign-changing blowing-up solutions for the critical nonlinear heat equation
Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two
Strongly anisotropic type II blow up at an isolated point
On spectral theory for Schrödinger operators with strongly singular potentials
Boundedness of global solutions for a supercritical semilinear heat equation and its application