Dissipative reaction diffusion systems with quadratic growth

Dissipative reaction diffusion systems with quadratic growth

We introduce a class of reaction diffusion systems of which weak solution exists global-in-time with relatively compact orbit in L. Reaction term in this class is quasi-positive, dissipative, and up to with quadratic growth rate. If the space dimension is less than or equal to two, the solution is classical and uniformly bounded. Provided with the entropy structure, on the other hand, this weak...

Bifurcation Pattern in Reaction-Diffusion Dissipative Systems

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...

Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension

This paper is devoted to the study of the regularity of solutions to some systems of reaction– diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N . The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It al...

Attractors for Partly Dissipative Reaction Diffusion SYstems in R^n

In this paper, we study the asymptotic behavior of solutions for the partly dissipative reaction diffusion equations in ‫ޒ‬ n. We prove the asymptotic compact-ness of the solutions and then establish the existence of the global attractor in 2 Ž n .

Partly Dissipative Reaction-diffusion Systems and a Model of Phosphorus Diffusion in Silicon