Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R}

The author considers semilinear parabolic equations of the form u_t=u_xx+f(u),\quad x\in \mathbb R,t>0, where f a C^1 function. Assuming that 0 and \gamma >0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose init...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Poláčik, Peter
Format: Électronique eBook
Langue:Inglés
Publié: Providence : American Mathematical Society, 2020.
Collection:Memoirs of the American Mathematical Society ; no. 1278.
Sujets:
Reaction-diffusion equations.
Differential equations, Parabolic.
Differential equations, Partial.
Équations de réaction-diffusion.
Équations différentielles paraboliques.
Équations aux dérivées partielles.
Ecuaciones diferenciales
Ecuaciones de reacción-difusión
Differential equations, Parabolic
Differential equations, Partial
Reaction-diffusion equations
Partial differential equations > Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35] > Initial value problems for second-order parabolic equations.
Partial differential equations > Qualitative properties of solutions > Asymptotic behavior of solutions.
Partial differential equations > Qualitative properties of solutions > Stability.
Partial differential equations > Qualitative properties of solutions > Oscillation, zeros of solutions, mean value theorems, etc..
Accès en ligne:Texto completo
Table des matières:
  • Cover
  • Title page
  • Chapter 1. Introduction
  • Chapter 2. Main results
  • 2.1. Minimal systems of waves and propagating terraces
  • 2.2. The case where 0 and are both stable
  • 2.3. The case where one of the steady states 0, is unstable
  • 2.4. The \om-limit set and quasiconvergence
  • 2.5. Locally uniform convergence to a specific front and exponential convergence
  • Chapter 3. Phase plane analysis
  • 3.1. Basic properties of the trajectories
  • 3.2. A more detailed description of the minimal system of waves
  • 3.3. Some trajectories out of the minimal system of waves
  • 6.7. Completion of the proofs of Theorems 2.7, 2.9, 2.17
  • 6.8. Completion of the proofs of Theorems 2.11 and 2.19
  • 6.9. Proof of Theorem 2.22
  • Bibliography
  • Back Cover

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