Global Existence of Reaction-Diffusion System with Porous Medium Diffusion: A Note on Laamri-Pierre(2017) (IV)

Speaker:

Professor Tengfei Zhang, School of Mathematics and Physics, China University in Geosciences (Wuhan)

Description:

I will discuss some perspectives and analysis tools on reaction-diffusion systems, including particularly the sketch proof of Laamri-Pierre's article (2017) on L^1 weak solution. Their proof contains two type results. The main idea is to prove the nonlinear reaction terms are uniformly integrable. (i) if the nonliearities are bounded in L^1, then they use a renormalized technique to prove the existence, under the constraint of porous medium's power $(N-2)/N < m_i <2$. (N denotes the spatial dimension) (ii) if the nonliearities are uniformly bounded by some norms of unknowns with power less than $m_i +1$, they prove the result by a dual energy method. Their work may provide some motivations for our next work, and in this sense it is worthwhile to study the article and to learn their techniques.

Reference:

Laamri, El Haj, and Michel Pierre

"Global existence for reaction–diffusion systems with nonlinear diffusion and control of mass." Annales de l'Institut Henri Poincaré C, Analyse non linéaire. Vol. 34. No. 3. Elsevier Masson, 2017.

Topic:

Stochastic & Multiscale Modeling and Computation