A Permutation Related to Non-compact Global Attractors for Slowly Non-dissipative Systems

作者：Pimentel Juliana^*; Rocha Carlos

来源：Journal of Dynamics and Differential Equations, 2016, 28(1): 1-28.

DOI：10.1007/s10884-014-9414-x

• Global attractors
• Slowly non-dissipative equations
• Heteroclinic orbits
• Blow-up solutions

We consider scalar reaction-diffusion equations with non-dissipative nonlinearities generating global semiflows which exhibit blow-up in infinite time. This type of equations was only recently approached and the corresponding dynamical systems are known as slowly non-dissipative systems. The existence of unbounded solutions, referred to as grow-up solutions, requires the introduction of some objects interpreted as equilibria at infinity. By extending known results, we are able to obtain a complete decomposition of the associated non-compact global attractor. The connecting orbit structure is determined based on the Sturm permutation method, which yields a simple criterion for the existence of heteroclinic connections.

• 出版日期2016-3