On the Stability of Type I Blow Up For the Energy Super Critical Heat Equation
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Publication:5230268
DOI10.1090/memo/1255zbMath1430.35138arXiv1605.07337OpenAlexW4229561650WikidataQ127445633 ScholiaQ127445633MaRDI QIDQ5230268
Pierre Raphaël, Jérémie Szeftel, Charles Collot
Publication date: 21 August 2019
Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1605.07337
Stability in context of PDEs (35B35) Bifurcations in context of PDEs (35B32) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Semilinear elliptic equations (35J61) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)
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Cites Work
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- Codimension one threshold manifold for the critical gKdV equation
- Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space
- Type II blow up for the energy supercritical NLS
- On blowup in supercritical wave equations
- Stable self-similar blowup in energy supercritical Yang-Mills theory
- 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
- Construction of multi-soliton solutions for the \(L^2\)-supercritical gKdV and NLS equations
- Threshold and generic type I behaviors for a supercritical nonlinear heat equation
- On elliptic equations related to self-similar solutions for nonlinear heat equations
- Nonexistence of type II blowup solution for a semilinear heat equation
- Invariant manifolds and dispersive Hamiltonian evolution equations
- Selfsimilar expanders of the harmonic map flow
- Stability of the blow-up profile for equations of the type \(u_ t=\Delta u+| u| ^{p-1}u\)
- Stable blow up dynamics for the critical co-rotational wave maps and equivariant Yang-Mills problems
- Nonexistence of backward self-similar blowup solutions to a supercritical semilinear heat equation
- The existence of bounded solutions of a semilinear elliptic equation
- Non-generic blow-up solutions for the critical focusing NLS in 1-D
- Classification of type I and type II behaviors for a supercritical nonlinear heat equation
- On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics
- Asymptotic behavior of positive solutions of equation \(\Delta{} u+K(x)u^ p=0\) in \(\mathbb{R}{}^ n\)
- Refined uniform estimates at blow-up and applications for nonlinear heat equations
- A Liouville theorem for the critical generalized Korteweg-de Vries equation
- Semilinear elliptic equations and supercritical growth
- A nonlinear heat equation with singular initial data
- Type II blow-up for the four dimensional energy critical semi linear heat equation
- On melting and freezing for the 2D radial Stefan problem
- Blow up for the critical generalized Korteweg-de Vries equation. I: Dynamics near the soliton
- The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
- Type-II blowup for a semilinear heat equation
- Quasilinear Dirichlet problems driven by positive sources
- Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity
- Non-radial singular solutions of Lane-Emden equations in $R^N$
- Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension
- On stable self-similar blowup for equivariant wave maps
- Shrinkers, expanders, and the unique continuation beyond generic blowup in the heat flow for harmonic maps between spheres
- Nondegeneracy of blowup for semilinear heat equations
- Asymptotically self‐similar blow‐up of semilinear heat equations
- The Existence of Bounded Solutions of a Semilinear Heat Equation
- Type II Blow up Manifolds for the Energy Supercritical Semilinear Wave Equation
- On Nonexistence of type II blowup for a supercritical nonlinear heat equation
- Blow up rate for semilinear heat equations with subcritical nonlinearity
- Self-similar solutions to super-critical gKdV
- Stable blow up dynamics for energy supercritical wave equations
- Morse theory and infinite families of harmonic maps between spheres
