TY - CHAP
T1 - Nonlinear Evolution Equations and Their Application to Chemotaxis Models
AU - Kubo, Akisato
AU - Hoshino, Hiroki
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Recently, we have investigated the global existence in time and asymptotic profile of solutions of some nonlinear evolution equations with strong dissipation and proliferation arising in mathematical biology. In this chapter, we improve the asymptotic behaviour of the solution to a simpler equation so that its derivative with respect to t converges exponentially to a constant steady state. We apply our result to a chemotaxis model and show the global existence in time and such exponential convergence property of the solution.
AB - Recently, we have investigated the global existence in time and asymptotic profile of solutions of some nonlinear evolution equations with strong dissipation and proliferation arising in mathematical biology. In this chapter, we improve the asymptotic behaviour of the solution to a simpler equation so that its derivative with respect to t converges exponentially to a constant steady state. We apply our result to a chemotaxis model and show the global existence in time and such exponential convergence property of the solution.
UR - http://www.scopus.com/inward/record.url?scp=85065415384&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065415384&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-04459-6_32
DO - 10.1007/978-3-030-04459-6_32
M3 - Chapter
AN - SCOPUS:85065415384
T3 - Trends in Mathematics
SP - 337
EP - 347
BT - Trends in Mathematics
PB - Springer International Publishing
ER -