Study of ODE limit problems for reaction-diffusion equations

• Main Authors: Jacson Simsen, Mariza Stefanello Simsen, Aleksandra Zimmermann
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2018-01-01
• Series: Opuscula Mathematica
• Subjects: ODE limit problems; shadow systems; reaction-diffusion equations; parabolic problems; variable exponents; attractors; upper semicontinuity
• Online Access: http://www.opuscula.agh.edu.pl/vol38/1/art/opuscula_math_3807.pdf

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.