TY  - JOUR
ID  - Simsen2018
LB  - Simsen2018
AU  - Simsen, Jacson
AU  - Simsen, Mariza Stefanello
AU  - Zimmermann, Aleksandra
TI  - Study of ODE limit problems for reaction-diffusion equations
ST  - Study of ODE limit problems for reaction-diffusion equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 1
SP  - 117
EP  - 131
DO  - https://doi.org/10.7494/OpMath.2018.38.1.117
UR  - https://doi.org/10.7494/OpMath.2018.38.1.117
AB  - In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \(L^{\infty}(\Omega)\) and the diffusion coefficients go to infinity.
KW  - ODE limit problems
KW  - shadow systems
KW  - reaction-diffusion equations
KW  - parabolic problems
KW  - variable exponents
KW  - attractors
KW  - upper semicontinuity
SN  - 1232-9274
ER  -