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Sandra Lucente

Publications and source records attributed to Sandra Lucente.

9 recordsLinked to original sources
arXiv2026

Semilinear damped wave equation on a compact Lie group with a non-autonomous forcing term

In the present note, we consider a semilinear damped wave equation on a compact Lie group with a non-autonomous nonlinearity $φ(t)|u|^p$. We are interested in describing how the nonnegative time-dependent factor $φ$ affects the global in time prolongability of a local solution. In particular, the summability of the function $φ$ provides a criterion to distinguish between the blow-up in finite time and global existence of small data. Finally, we derive sharp lifespan estimates for local in time solutions when $φ\not\in L^1([0,+\infty)))$ and satisfies a certain scaling condition, that we named uniform upper scaling condition.

math.AP↗
arXiv2025

Singularity: a Seventh Memo?

In this paper we explore the relationships between Calvino's memos and Mathematics. In the first part, we discuss how Lightness, Quickness, Exactitude, Visibility, Multiplicity are present in the mathematical language, reasoning and in the work of the mathematician. In addiction, we follow a similar path for the topics of Calvino's lecture of which we only know the title or some notes. In the final part, we explain why `Singularity' could be chosen as a possible topic for Calvino's seventh lecture.

math.HO↗
arXiv2021

Fujita modified exponent for scale invariant damped semilinear wave equations

The aim of this paper is to prove a blow up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise decay order of the initial data. In addition we give an upper bound estimate for the lifespan of the solution, in terms of the power of the nonlinearity, size and growth of initial data.

math.AP↗
arXiv2020

Nonexistence of global solutions for generalized Tricomi equations with combined nonlinearity

In the present paper, we investigate the blow-up dynamics for local solutions to the semilinear generalized Tricomi equation with combined nonlinearity. As a result, we enlarge the blow-up region in comparison to the ones for the corresponding semilinear models with either power nonlinearity or nonlinearity of derivative type. Our approach is based on an iteration argument to establish lower bound estimates for the space average of local solutions. Finally, we obtain upper bound estimates for the lifespan of local solutions as byproduct of our iteration argument.

math.AP↗
arXiv2020

A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type

In this note, we prove a blow-up result for a semilinear generalized Tricomi equation with nonlinear term of derivative type, i.e., for the equation $\mathscr{T}_{\!\!\ell} u = |\partial_t u|^p$, where $ \mathscr{T}_{\!\!\ell} = \partial_t^2-t^{2\ell}Δ$. Smooth solutions blow up in finite time for positive Cauchy data when the exponent $p$ of the nonlinear term is below $\frac{\mathscr{Q}}{\mathscr{Q}-2}$, where $\mathscr{Q}=(\ell+1)n+1$ is the quasi-homogeneous dimension of the generalized Tricomi operator $\mathscr{T}_{\!\!\ell}$. Furthermore, we get also an upper bound estimate for the lifespan.

math.AP↗
arXiv2014

From $p_0(n)$ to $p_0(n+2)$

In this note we study the global existence of small data solutions to the Cauchy problem for the semi-linear wave equation with a not effective scale-invariant damping term, namely \[ v_{tt}-\triangle v + \frac2{1+t}\,v_t = |v|^p, \qquad v(0,x)=v_0(x),\quad v_t(0,x)=v_1(x), \] where $p>1$, $n\ge 2$. We prove blow-up in finite time in the subcritical range $p\in(1,p_2(n)]$ and an existence result for $p>p_2(n)$, $n=2,3$. In this way we find the critical exponent for small data solutions to this problem. All these considerations lead to the conjecture $p_2(n)=p_0(n+2)$ for $n\ge2$, where $p_0(n)$ is the Strauss exponent for the classical wave equation.

math.AP↗
arXiv2012

A modified test function method for damped waves

In this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solution.

math.AP↗
arXiv2012

Semi-linear wave equations with effective damping

We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical case.

math.AP↗