Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\... more Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\Omega$ is assumed to be a $\mathcal{C}^4$-hypersurface. In this paper we consider the initial-boundary value problem associated with the following thermoelastic plate system \[ \begin{cases} \partial_t^2u +\Delta^2 u+\Delta\theta=f(u),\ & x\in\Omega,\ t>0, \\ \partial_t\theta-\Delta \theta-\Delta \partial_tu=0,\ & x\in\Omega,\ t>0, \end{cases} \] subject to boundary conditions \[ \begin{cases} u=\Delta u=0,\ & x\in\partial\Omega,\ t>0,\\ \theta=0,\ & x\in\partial\Omega,\ t>0, \end{cases} \] and initial conditions \[ u(x,0)=u_0(x),\ \partial_tu(x,0)=v_0(x)\ \mbox{and}\ \theta(x,0)=\theta_0(x),\ x\in\Omega. \] We calculate explicit the fractional powers of the thermoelastic plate operator associated with this system via Balakrishnan integral formula and we present a fractional approximated system. We obtain a result of local well-posedness of the thermoelastic plate system and ...
In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partia... more In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partial_t u =- u + g \left(\beta(t)(Ku) \right)\ \ \mbox{in}\ \ \Omega,\\ u = 0\ \ \mbox{in}\ \ \mathbb{R}^N\backslash\Omega, \end{cases} \] where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $\beta$ denotes the functional parameter given by a continuous bounded function on $\mathbb{R}$, and $K$ is an integral operator with symmetric kernel. We prove existence and some regularity properties of the pullback attractor.
Neste trabalho estudamos a dinâmica assintótica não linear de algumas equações parabólicas do tip... more Neste trabalho estudamos a dinâmica assintótica não linear de algumas equações parabólicas do tipo reação-difusão sob perturbações nos parâmetros e perturbações singulares no domínio do tipo dumbbell. Mais precisamente, trataremos dos atratores ...
In this work we consider the non local evolution equation with time-dependent terms which arises ... more In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in $\mathbb{R}^N$ \[ \partial_t u=- u + g \left(\beta(J*u) +\beta h(t,u)\right) \] under some restrictions on $h$, growth restrictions on the nonlinear term $g$ and $\beta>1$. We prove, under suitable assumptions, existence, regularity and upper-semicontinuity of pullback attractors with respect to functional parameter $h(t)$ in some weighted spaces.
In this work we consider the Dirichlet problem governed by a non local evolution equation. We pro... more In this work we consider the Dirichlet problem governed by a non local evolution equation. We prove the existence of exponential attractors for the flow generated by this problem, and as a consequence we obtain the finite dimensionality of the global attractor whose existence was proved in [1]
Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\... more Let $\Omega$ be a bounded domain in $\mathbb{R}^N$ with $N\geqslant 2$, which boundary $\partial\Omega$ is assumed to be a $\mathcal{C}^4$-hypersurface. In this paper we consider the initial-boundary value problem associated with the following thermoelastic plate system \[ \begin{cases} \partial_t^2u +\Delta^2 u+\Delta\theta=f(u),\ & x\in\Omega,\ t>0, \\ \partial_t\theta-\Delta \theta-\Delta \partial_tu=0,\ & x\in\Omega,\ t>0, \end{cases} \] subject to boundary conditions \[ \begin{cases} u=\Delta u=0,\ & x\in\partial\Omega,\ t>0,\\ \theta=0,\ & x\in\partial\Omega,\ t>0, \end{cases} \] and initial conditions \[ u(x,0)=u_0(x),\ \partial_tu(x,0)=v_0(x)\ \mbox{and}\ \theta(x,0)=\theta_0(x),\ x\in\Omega. \] We calculate explicit the fractional powers of the thermoelastic plate operator associated with this system via Balakrishnan integral formula and we present a fractional approximated system. We obtain a result of local well-posedness of the thermoelastic plate system and ...
In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partia... more In this paper we consider the non local non autonomous evolution problem \[ \begin{cases} \partial_t u =- u + g \left(\beta(t)(Ku) \right)\ \ \mbox{in}\ \ \Omega,\\ u = 0\ \ \mbox{in}\ \ \mathbb{R}^N\backslash\Omega, \end{cases} \] where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $\beta$ denotes the functional parameter given by a continuous bounded function on $\mathbb{R}$, and $K$ is an integral operator with symmetric kernel. We prove existence and some regularity properties of the pullback attractor.
Neste trabalho estudamos a dinâmica assintótica não linear de algumas equações parabólicas do tip... more Neste trabalho estudamos a dinâmica assintótica não linear de algumas equações parabólicas do tipo reação-difusão sob perturbações nos parâmetros e perturbações singulares no domínio do tipo dumbbell. Mais precisamente, trataremos dos atratores ...
In this work we consider the non local evolution equation with time-dependent terms which arises ... more In this work we consider the non local evolution equation with time-dependent terms which arises in models of phase separation in $\mathbb{R}^N$ \[ \partial_t u=- u + g \left(\beta(J*u) +\beta h(t,u)\right) \] under some restrictions on $h$, growth restrictions on the nonlinear term $g$ and $\beta>1$. We prove, under suitable assumptions, existence, regularity and upper-semicontinuity of pullback attractors with respect to functional parameter $h(t)$ in some weighted spaces.
In this work we consider the Dirichlet problem governed by a non local evolution equation. We pro... more In this work we consider the Dirichlet problem governed by a non local evolution equation. We prove the existence of exponential attractors for the flow generated by this problem, and as a consequence we obtain the finite dimensionality of the global attractor whose existence was proved in [1]
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