Hair-triggered instability of radial steady states, spread and extinction in semilinear heat equations
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Publication:859508
DOI10.1016/j.jde.2006.06.008zbMath1387.35333OpenAlexW2094373337MaRDI QIDQ859508
Publication date: 16 January 2007
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2006.06.008
Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Classical flows, reactions, etc. in chemistry (92E20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Initial value problems for second-order parabolic equations (35K15) Initial value problems for second-order parabolic systems (35K45)
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Cites Work
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- Reaction-diffusion waves in an isothermal chemical system with general orders of autocatalysis and spatial dimension
- Nonstabilizing solutions and grow-up set for a supercritical semilinear diffusion equation.
- Stability of traveling waves with criticals speeds for \(P\)-degree Fisher-type equations
- On ground state solutions of \(-\Delta{} u=u^ p-u^ q\)
- Asymptotic behavior of positive solutions of equation \(\Delta{} u+K(x)u^ p=0\) in \(\mathbb{R}{}^ n\)
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- Multidimensional nonlinear diffusion arising in population genetics
- On a conjecture of De Giorgi and some related problems
- Global existence for reaction-diffusion systems modelling ignition
- Exact multiplicity of positive solutions for a class of semilinear problems
- On bounded and unbounded global solutions of a supercritical semilinear heat equation
- Existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations
- Exact multiplicity of positive solutions for a class of semilinear problem. II
- On the stability of radial solutions of semilinear elliptic equations in all of \(\mathbb R^n\)
- Allee effect and bistability in a spatially heterogeneous predator-prey model
- Global Existence, Large Time Behavior and Life Span of Solutions of a Semilinear Parabolic Cauchy Problem
- On the stability and instability of positive steady states of a semilinear heat equation in ℝn
- On the Cauchy Problem for Reaction-Diffusion Equations
- The global dynamics of isothermal chemical systems with critical nonlinearity
- On Nonexistence of type II blowup for a supercritical nonlinear heat equation
- Some remarks on Liouville type results for quasilinear elliptic equations
- Sharp transition between extinction and propagation of reaction
- Further study on a nonlinear heat equation
