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Pullback dynamics for a semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains
Gleiciane S. Aragão, Flank D. M. Bezerra, Lucas G. Mendonça
We are interested in studying a non-autonomous semilinear heat equation with homogeneous Neumann boundary conditions on time-varying domains. Using a differential geometry approach…
Upper semicontinuity for a class of nonlocal evolution equations with Neumann condition
Flank D. M. Bezerra, Silvia Sastre-Gomez, Severino H. da Silva
In this paper we consider the following nonlocal autonomous evolution equation in a bounded domain in \[ \partial_t u(x,t) =- h(x)u(x,t) + g \Big(\int_Ω J(x,y)u(…
Fractional powers approach of operators for higher order abstract Cauchy problems
Flank D. M. Bezerra, Lucas A. Santos
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of…
Well-posedness for some third-order evolution differential equations: A semigroup approach
Flank D. M. Bezerra, Alexandre N. Carvalho, Lucas A. Santos
In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + ηA^{\frac13} u_{tt} +ηA^{\frac23} u_…
Fractional oscillon equations; solvability and connection with classical oscillon equations
Flank D. M. Bezerra, Rodiak N. Figueroa-López, Marcelo J. D. Nascimento
In this paper we are concerned with the asymptotic behavior of nonautonomous fractional approximations of oscillon equation $$ u_{tt}-μ(t)Δu+ω(t)u_t=f(u),\ x\inΩ,\ t\in\mathbb{R},…
Continuity of the set equilibria of non-autonomous damped wave equations with terms concentrating on the boundary
Flank D. M. Bezerra, Gleiciane da Silva Aragão
In this paper we are interested in the behavior of the solutions of non-autonomous damped wave equations when some reaction terms are concentrated in a neighborhood of the boundary…