Periodic Orbits and Attractors for Autonomous Reaction-Diffusion Systems

Matthias Büger
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Matthias Büger: Mathematisches Institut der Justus-Liebig-Universität Gießen

A chapter in Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 2001, pp 753-773 from Springer

Abstract: Abstract The dynamics of solutions of one autonomous reaction-diffusion equation % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWaaSaaaeaacqWGKbazaeaacqWGKbazcqWG0baD % aaGaemyEaKNaeyypa0teduuDJXwAKbYu51MyVXgaiyaacqWF7oaBii % GacqGFuoarcqWG5bqEcqGHRaWkcqWGNbWzcqGGOaakcqWG5bqEcqGG % Paqkaaa!5184! $$ \frac{d} {{dt}}y = \lambda \Delta y + g(y) $$ with Dirichlet or other boundary conditions on an interval Q= (0,1) has been examined by many authors [6], [8], [9], [12], [17]. In this case, all solutions converge to the set of stationary points.

Keywords: Periodic Solution; Periodic Orbit; Global Attractor; Planar Solution; Zero Solution (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-3-642-56589-2_30

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