A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity

作者：Lankeit, Johannes^*

来源：Mathematical Methods in the Applied Sciences, 2016, 39(3): 394-404.

DOI：10.1002/mma.3489

• chemotaxis
• singular sensitivity
• global existence
• boundedness

We consider the parabolic chemotaxis model @@@ {u(t) = Delta u - chi del .(u/v del v) @@@ v(t) = Delta v - v + u @@@ in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for chi is an element of E (0, chi(0)) for some chi(0) > 1, thereby proving that the value chi = 1 is not critical in this regard. Our main tool is consideration of the energy functional @@@ F-a,F-b(u, v) = integral(Omega) u ln u - a integral(Omega) u ln u + b integral(Omega) vertical bar del root v vertical bar(2) @@@ for a > 0, b >= 0, where using nonzero values of b appears to be new in this context.

• 出版日期2016-2