TY - JOUR
T1 - Well posedness and asymptotic behavior of supercritical reaction-diffusion equations with nonlinear boundary conditions
AU - Rodríguez-Bernal, Aníbal
AU - Vidal-López, Alejandro
N1 - Publisher Copyright:
© 2016 International Press.
PY - 2016
Y1 - 2016
N2 - We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a dissipative system. Assuming this balance, the dynamics of the solutions is the same that takes place in subcritical spaces since their attractors coincide.
AB - We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a dissipative system. Assuming this balance, the dynamics of the solutions is the same that takes place in subcritical spaces since their attractors coincide.
KW - Local existence
KW - Nonlinear balance
UR - http://www.scopus.com/inward/record.url?scp=85006700458&partnerID=8YFLogxK
U2 - 10.4310/DPDE.2016.v13.n4.a1
DO - 10.4310/DPDE.2016.v13.n4.a1
M3 - Article
AN - SCOPUS:85006700458
SN - 1548-159X
VL - 13
SP - 273
EP - 295
JO - Dynamics of Partial Differential Equations
JF - Dynamics of Partial Differential Equations
IS - 4
ER -