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Lucas A. Santos

Publications and source records attributed to Lucas A. Santos.

5 recordsLinked to original sources
arXiv2024

Boundedness of solutions of nonautonomous degenerate logistic equations

In this work we analyze the boundedness properties of the solutions of a nonautonomous parabolic degenerate logistic equation in a bounded domain. The equation is degenerate in the sense that the logistic nonlinearity vanishes in a moving region, $K(t)$, inside the domain. The boundedness character of the solutions depends not only on, roughly speaking, the first eigenvalue of the Laplace operator in $K(t)$ but also on the way this moving set evolves inside the domain and in particular on the speed at which it moves.

math.AP↗
arXiv2021

Fractional powers approach of operators for higher order abstract Cauchy problems

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 the second kind to obtain results of existence, regularity and behavior asymptotic of solutions for linear abstract evolution equations of $n$-th order in time, where $n\geqslant3$. We also prove generalizations of classical results on structural damping for linear systems of differential equations.

math.AP↗
arXiv2021

Well-posedness for some third-order evolution differential equations: A semigroup approach

In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time $$ u_{ttt} +A u + ηA^{\frac13} u_{tt} +ηA^{\frac23} u_t=f(u) $$ where $η>0$, $X$ is a separable Hilbert space, $A:D(A)\subset X\to X$ is an unbounded sectorial operator with compact resolvent, and for some $λ_0>0$ we have $\mbox{Re}σ(A)>λ_0$ and $f:D(A^{\frac13})\subset X\to X$ is a nonlinear function with suitable conditions of growth and regularity.

math.AP↗