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Singular quasilinear convective systems involving variable exponents

Moussaoui Abdelkrim, Nabab Dany, Vélin Jean

Opuscula Mathematica

2024

Vol. 44, no. 1

105--134

The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder’s fixed point theorem.

Reaction-diffusion coupled inclusions with variable exponents and large diffusion

Simsen Jacson, Stefanello Simsen Mariza, Wittbold Petra

Opuscula Mathematica

2021

Vol. 41, no. 4

539--570

This work concerns the study of asymptotic behavior of coupled systems of p(x)-Laplacian differential inclusions. We obtain that the generalized semiflow generated by the coupled system has a global attractor, we prove continuity of the solutions with respect to initial conditions and a triple of parameters and we prove upper semicontinuity of a family of global attractors for reaction-diffusion systems with spatially variable exponents when the exponents go to constants greater than 2 in the topology of [formula] and the diffusion coefficients go to infinity.

Study of ODE limit problems for reaction-diffusion equations

Simsen J., Simsen M. S., Zimmermann A.

Opuscula Mathematica

2018

Vol. 38, no. 1

117--131

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 [formula] and the diffusion coefficients go to infinity.