Global existence of solutions to reaction–diffusion systems without conditions on the nonlinearities growth

✍ Scribed by Said Kouachi

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 97 KB
• Volume: 34
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1401

✦ Synopsis

It is well known that, for reaction-diffusion systems, if the nonlinearities grow faster than a polynomial, nothing seems to be known for instance. The purpose of this paper is to give sufficient conditions guaranteeing global existence, uniqueness and uniform boundedness of solutions for coupled reaction-diffusion equations without condition growth on the reactions terms f and g in case f +g = 0. These systems possess many and various applications in physics as the diffusion of the Phosphorus in the Silicone or some models describing some nuclear reactions; there have also been other applications in chemistry and biology. Our techniques are based on the Lyapunov functional methods. Copyright