Jacson Simsen
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View article: Strongly order preserving multivalued nonautonomous dynamical systems
Strongly order preserving multivalued nonautonomous dynamical systems Open
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete traj…
View article: Monotone Multivalued Nonautonomous Dynamical Systems
Monotone Multivalued Nonautonomous Dynamical Systems Open
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete traj…
View article: Evolution equations on time-dependent Lebesgue spaces with variable exponents
Evolution equations on time-dependent Lebesgue spaces with variable exponents Open
We extend the results in Kloeden-Simsen [CPAA 2014] to \(p(x,t)\)-Laplacian problems on time-dependent Lebesgue spaces withvariable exponents. We study the equation $$\displaylines{ \frac{\partial u_\lambda}{\partial t}(t)-\operatorname{di…
View article: Robustness for coupled inclusions with respect to variable exponents
Robustness for coupled inclusions with respect to variable exponents Open
This work concerns the study of the stability of the solutions and the robustness of the global attractors with respect to the variation of spatially variable exponents for a system with three inclusions. We prove the continuity of the flo…
View article: Homogenization process for a semi-diffusive coupled inclusion system
Homogenization process for a semi-diffusive coupled inclusion system Open
This work concerns the study of homogenization for a semi-diffusive system of inclusions with large diffusion and variable exponents. We show that under certain conditions the asymptotic dynamics is determined by an ordinary differential c…
View article: Stability for evolution equations with variable growth
Stability for evolution equations with variable growth Open
We study the character of dependence on the data and the nonlinear structure of the equation for the solutions of the homogeneous Dirichlet problem for the evolution $p(x,t)$-Laplacian with the nonlinear source \[ u_t-Δ_{p(x,t)}u=f(x,t,u),…
View article: Coupled nonautonomous inclusion systems with spatially variable exponents
Coupled nonautonomous inclusion systems with spatially variable exponents Open
A family of nonautonomous coupled inclusions governed by $p(x)$-Laplacian operators with large diffusion is investigated. The existence of solutions and pullback attractors as well as the generation of a generalized process are established…
View article: Reaction-diffusion coupled inclusions with variable exponents and large diffusion
Reaction-diffusion coupled inclusions with variable exponents and large diffusion Open
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 th…
View article: Convergence of quasilinear parabolic equations to semilinear equations
Convergence of quasilinear parabolic equations to semilinear equations Open
In this work we consider a family of reaction-diffusion equations with variable exponents reaching as a limit problem a semilinear equation. We provide uniform estimates for the solutions and we prove that the solutions of the family of qu…
View article: Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions
Convergence of nonautonomous multivalued problems with large diffusion to ordinary differential inclusions Open
In this work we consider a family of nonautonomous partial differential inclusions governed by $ p $-laplacian operators with variable exponents and large diffusion and driven by a forcing nonlinear term of Heaviside type. We prove first t…
View article: Asymptotic behavior of coupled inclusions with variable exponents
Asymptotic behavior of coupled inclusions with variable exponents Open
This work concerns the study of asymptotic behavior of the solutions of a nonautonomous coupled inclusion system with variable exponents. We prove the existence of a pullback attractor and that the system of inclusions is asymptotically au…
View article: Differential inclusion for the evolution p(x)-Laplacian with memory
Differential inclusion for the evolution p(x)-Laplacian with memory Open
We consider the evolution differential inclusion for a nonlocal operator that involves p(x)-Laplacian, $$ u_t-\Delta_{p(x)} u-\int_0^{t}g(t-s)\Delta_{p(x)} u(x,s)\,ds\in \mathbf{F}(u) \quad \text{in } Q_T=\Omega\times (0,T), $$ where $\Ome…
View article: Weak upper semicontinuity of pullback attractors for nonautonomous reaction-diffusion equations
Weak upper semicontinuity of pullback attractors for nonautonomous reaction-diffusion equations Open
We consider nonautonomous reaction-diffusion equations with variable exponents and large diffusion and we prove continuity of the flow and weak upper semicontinuity of a family of pullback attractors when the exponents go to $2$ in $L^\inf…
View article: Differential inclusion for the evolution p(x)-laplacianwith memory
Differential inclusion for the evolution p(x)-laplacianwith memory Open
This work was initiated when the authors were supported by the research grants CSF-CAPES-PVE-Process 88881.030388/2013-01 and the program “Science Without Borders”, CSF-CAPES-PVE-Process 88887.059583/2014-00, Brazil. The first author was s…
View article: Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces
Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces Open
We study the homogeneous Dirichlet problem for the class of nonlinear parabolic equations with variable nonlinearity [Formula: see text] in the cylinder [Formula: see text] with given nonnegative weights [Formula: see text], [Formula: see …
View article: On asymptotically autonomous dynamics for multivalued evolution problems
On asymptotically autonomous dynamics for multivalued evolution problems Open
In this work we improve the result presented by Kloeden-Simsen-Stefanello Simsen in [8] by reducing uniform conditions. We prove theoretical results in order to establish convergence in the Hausdorff semi-distance of the component subsets …
View article: Non-autonomous reaction-diffusion equations with variable exponents and large diffusion
Non-autonomous reaction-diffusion equations with variable exponents and large diffusion Open
In this work we prove continuity of solutions with respect to initial conditions and a couple of parameters and we prove upper semicontinuity of a family of pullback attractors for the problem \begin{document}$\left\{ {\begin{array}{*{2…
View article: Robustness with respect to exponents for nonautonomous reaction–diffusion equations
Robustness with respect to exponents for nonautonomous reaction–diffusion equations Open
In this work we consider a family of nonautonomous problems with homogeneous Neumann boundary conditions and spatially variable exponents with equation of the form \begin{equation*} \frac{\partial u_{\lambda}}{\partial_t}(t)-\operatorname{…
View article: Study of ODE limit problems for reaction-diffusion equations
Study of ODE limit problems for reaction-diffusion equations Open
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 f…
View article: A Takeuchi-Yamada type equation with variable exponents
A Takeuchi-Yamada type equation with variable exponents Open
We prove continuity of the flows and upper semicontinuity of globalattractors for a Takeuchi-Yamada type equation with variableexponents.
View article: Global attractors for $p$-Laplacian differential inclusions in unbounded domains
Global attractors for $p$-Laplacian differential inclusions in unbounded domains Open
In this work we consider a differential inclusion governed by a p-Laplacianoperator with a diffusion coefficient depending on a parameter in which thespace variable belongs to an unbounded domain. We prove the existence of aglobal attracto…
View article: Reaction-Diffusion equations with spatially variable exponents and large diffusion
Reaction-Diffusion equations with spatially variable exponents and large diffusion Open
In this work we prove continuity of solutions with respect toinitial conditions and couple parameters and we prove joint uppersemicontinuity of a family of global attractors for the problem\begin{eqnarray}&\frac{\partial u_{s}}{\partialt}(…