Finite time blow-up and global solutions for a nonlocal parabolic equation with Hartree type nonlinearity
DOI10.3934/cpaa.2020134zbMath1446.35060OpenAlexW3013278599MaRDI QIDQ2176993
Publication date: 6 May 2020
Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/cpaa.2020134
global existencestationary solutionfinite time blow-upnonlocal parabolic equationhigh initial energy
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian (35K91)
Cites Work
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- Sharp threshold of global existence and instability of standing wave for the Schrödinger-Hartree equation with a harmonic potential
- Global existence and blow-up results for a classical semilinear parabolic equation
- Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations
- On global solution to the Klein-Gordon-Hartree equation below energy space
- Transversality of stable and Nehari manifolds for a semilinear heat equation
- Stable and unstable sets for evolution of parabolic and hyperbolic type
- Invariant sets and the blow up threshold for a nonlocal equation of parabolic type
- Blow up threshold for a parabolic type equation involving space integral and variational structure
- Local vs. non-local interactions in population dynamics
- Convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations
- Persistence of wavefronts in delayed nonlocal reaction-diffusion equations
- Strong instability of standing waves for a nonlocal Schrödinger equation
- Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level.
- Global well-posedness and scattering for the mass-critical Hartree equation with radial data
- Saddle points and instability of nonlinear hyperbolic equations
- Boundedness of trajectories of parabolic equations and stationary solutions via dynamical methods
- Elliptic partial differential equations of second order
- Finite time blow-up and global existence for the nonlocal complex Ginzburg-Landau equation
- Global existence and finite time blow-up for a class of thin-film equation
- Blow-up and lifespan of solutions to a nonlocal parabolic equation at arbitrary initial energy level
- Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
- Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
- Global existence and blow-up of solutions to a class of nonlocal parabolic equations
- Energy scattering for a Klein-Gordon equation with a cubic convolution
- On global solution of nonlinear hyperbolic equations
- Stability of standing waves for the Klein–Gordon–Hartree equation
- Vacuum isolating, blow up threshold, and asymptotic behavior of solutions for a nonlocal parabolic equation
- The problem of uniqueness of the limit in a semilinear heat equation
- Thermal runaway in a non-local problem modelling Ohmic heating. Part II: General proof of blow-up and asymptotics of runaway
- On the nonlinear equations Δ𝑢+𝑒^{𝑢}=0 and ∂𝑣/∂𝑡=Δ𝑣+𝑒^{𝑣}
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