On \(\sqrt{\log\log}\) blow-up in higher-order reaction-diffusion and wave equations: A formal ``geometric approach
DOI10.1016/j.physd.2009.05.010zbMath1178.35082OpenAlexW2078401510MaRDI QIDQ842987
Publication date: 28 September 2009
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2009.05.010
similarity solutionsone space dimensionzero Dirichlet boundary conditionsnon-self-similar blow-upnonlinear critical Schrödinger equationPetrovskii's regularity criterionplasma physics parabolic equations
Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Second-order nonlinear hyperbolic equations (35L70) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Blow-up in context of PDEs (35B44)
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Cites Work
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- Variational approach to complicated similarity solutions of higher-order nonlinear PDEs. II
- On the formation of singularities in the curve shortening flow
- Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
- Local structure of the self-focusing singularity of the nonlinear Schrödinger equation
- Higher order nonlinear degenerate parabolic equations
- Singular ring solutions of critical and supercritical nonlinear Schrödinger equations
- On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach
- The normalized curve shortening flow and homothetic solutions
- Blow-up of solutions of nonlinear degenerate parabolic equations
- The interaction representation in the self-focusing theory
- Computer simulation of wave collapses in the nonlinear Schrödinger equation
- A stability technique for evolution partial differential equations. A dynamical systems approach
- Profiles and quantization of the blow up mass for critical nonlinear Schrödinger equation
- Asymptotic shape of cusp singularities in curve shortening
- On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
- Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
- The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
- Existence and stability of the log-log blow-up dynamics for the \(L^2\)-critical nonlinear Schrödinger equation in a domain
- Existence and stability of a solution blowing up on a sphere for an \(L^2\)-supercritical nonlinear Schrödinger equation
- Global solutions of higher-order semilinear parabolic equations in the supercritical range
- Proof of a spectral property related to the singularity formation for the \(L^{2}\) critical nonlinear Schrödinger equation
- Uniqueness of the ground state solution for \(\Delta u - u + u^3=0\) and a variational characterization of other solutions
- Asymptotics of Multibump Blow-up Self-Similar Solutions of the Nonlinear Schrödinger Equation
- Scaling, stability and singularities for nonlinear, dispersive wave equations: the critical case
- Shock waves and compactons for fifth-order non-linear dispersion equations
- The formation of shocks and fundamental solution of a fourth-order quasilinear Boussinesq-type equation
- Third-order nonlinear dispersive equations: Shocks, rarefaction, and blowup waves
- Similarity solutions of a higher order nonlinear diffusion equation
- Rate of $L^2$-concentration of blow-up solutions for critical nonlinear Schrödinger equation
- On a sharp lower bound on the blow-up rate for the 𝐿² critical nonlinear Schrödinger equation
- Source-type solutions of the fourth-order unstable thin film equation
- On the formation of singularities in solutions of the critical nonlinear Schrödinger equation
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