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 Annali dell'Universita di FerraraJournal Prestige (SJR): 0.429 Number of Followers: 0      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0430-3202 - ISSN (Online) 1827-1510 Published by Springer-Verlag  [2469 journals]
• Uniqueness and nullity of complete spacelike hypersurfaces immersed in the
anti-de Sitter space

Abstract: Abstract Our aim in this paper is to study the uniqueness of complete spacelike hypersurfaces immersed in the anti-de Sitter space $${{\mathbb {H}}}_1^{n+1}$$ , through the behavior of their higher order mean curvatures. This is done by applying a suitable maximum principle concerning smooth vector fields whose norm is Lebesgue integrable on a complete Riemannian manifold. We also infer the nullity of complete r-maximal spacelike hypersurfaces and, in particular, we establish a nonexistence result concerning complete 1-maximal spacelike hypersurfaces in $${{\mathbb {H}}}_1^{n+1}$$ .
PubDate: 2022-05-18

• Stability and boundedness criteria of solutions of a certain system of
second order differential equations

Abstract: Abstract This paper provides sufficient conditions for the stability, asymptotic stability, uniform stability, boundedness and uniformly boundedness of solutions of a certain class of second-order nonlinear vector differential equations using the second method of Lyapunov. By constructing a suitable complete Lyapunov function, which serves as a basic tool, we establish the properties mentioned above and thereby improve and complement some known results found in the literature. Lastly, the correctness of our main results is justified by the examples given.
PubDate: 2022-05-03

• Strictly hyperbolic Cauchy problems on $${\varvec{{\mathbb {R}}^n}}$$ R n
with unbounded and singular coefficients

Abstract: Abstract We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on $$(0,T]\times {\mathbb {R}}^n$$ in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in x with their x-derivatives and t-derivative of order $$\text {O}(t^{-\delta }),\delta \in [0,1),$$ and $$\text {O}(t^{-1})$$ respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at $$t=0$$ . We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution experiences a finite loss in the Sobolev space index in relation to the initial datum defined in the Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds $$O(t^{-1})$$ . We confirm this by providing a counterexample. Further, using the $$L^1$$ integrability of the logarithmic singularity in t and the global properties of the operator with respect to x, we derive an anisotropic cone condition in our setting.
PubDate: 2022-05-01

• Stability analysis for a multi-layer Hele-Shaw displacement

Abstract: Abstract A well known approximation for the displacement of two immiscible fluids in a porous medium is the Hele-Shaw model. In experiments it was observed that a liquid with variable viscosity, introduced between the two initial fluids, can minimize the Saffman-Taylor instability. In some works an attempt was made to replace the variable viscosity liquid with a sequence of several immiscible liquids with constant viscosities. We prove that the linear stability analysis of this multi-layer Hele-Shaw model leads us to an ill-posed problem.
PubDate: 2022-05-01

• Weak solutions for nonlinear waves in adhesive phenomena

Abstract: Abstract We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in arbitrary dimension as well as the case of non-local operators (e.g. fractional Laplacian).
PubDate: 2022-04-11

• X-generalized skew derivations with annihilating and centralizing
conditions in prime rings

Abstract: Abstract Let R be a prime ring of char $$(R)\ne 2$$ , $$Q_r$$ its right Martindale quotient ring and C its extended centroid, $$f(x_1,\dots , x_n)$$ a multilinear polynomial over C that is noncentral-valued on R and F an X-generalized skew derivation of R. If for some $$0\ne a\in R$$ , \begin{aligned} a[F(f(x_1,\dots , x_n)),f(x_1,\dots , x_n)]\in C \end{aligned} for all $$x_1,\dots , x_n\in R$$ , then one of the following holds: There exists $$\lambda \in C$$ such that $$F(x) = \lambda x$$ for all $$x \in R$$ ; There exist $$\lambda \in C$$ and $$a'\in Q_r$$ such that $$F(x) =a'x+xa'+ \lambda x$$ for all $$x \in R$$ and $$f(x_1,\dots , x_n)^2$$ is central-valued on R; R satisfies $$s_4$$ and there exist $$\lambda \in C$$ and $$a'\in Q_r$$ such that $$F(x) =a'x+xa'+ \lambda x$$ for all $$x \in R$$ .
PubDate: 2022-04-06

• An excellent derivative-free multiple-zero finding numerical technique of
optimal eighth order convergence

Abstract: Abstract A number of higher order Newton-like methods (i.e. the methods requiring both function and derivative evaluations) are available in literature for multiple zeros of a nonlinear function. However, higher order Traub-Steffensen-like methods (i.e. the methods requiring only function evaluations) for computing multiple zeros are rare in literature. Traub-Steffensen-like iterations are important in the circumstances when derivatives are complicated to evaluate or expensive to compute. Motivated by this fact, here we present an efficient and rapid-converging Traub-Steffensen-like algorithm to locate multiple zeros. The method achieves eighth order convergence by using only four function evaluations per iteration, therefore, this convergence rate is optimal. Performance is demonstrated by applying the method on different problems including some real life models. The computed results are compared with that of existing optimal eighth-order Newton-like techniques to reveal the computational efficiency of the new approach.
PubDate: 2022-04-04

• General decay of Bresse system by modified thermoelasticity of type III

Abstract: Abstract In this paper we have studied the model for arched beams problem \begin{aligned}&\rho _{1}\varphi _{tt}-k(\varphi _{x}+\psi +l\omega )_{x}-k_{0}l(\omega _{x}-l\varphi )=0,\\&\rho _{2}\psi _{tt}-b\psi _{xx}+k(\varphi _{x}+\psi +l\omega )+\gamma \theta _{tx}=0,\\&\rho _{1}\omega _{tt}-k_{0}(\omega _{x}-l\varphi )_{x}+kl(\varphi _{x} +\psi +l\omega )=0,\\&\rho _{3}\theta _{tt}-\kappa \theta _{xx}+\beta (g*\theta _{xx})+\gamma \psi _{tx}=0, \end{aligned} which reduces to the classical Timoshenko system when the arch curvature $$l=0$$ , the asymptotic stability of one-dimensional Timoshenko system by thermoelasticity of type III was proved by Djebabla and Tatar in Djebabla (J. Dyn. Control Syst. 16(2):189-210, 2010). The subject of this paper is to supplement these previous results by proving that the Bresse system which is considered a generalization of the Timoshenko system, is also subjected to the same sufficient condition that controls the stability of the Timoshenko system and we have shown that (exponential / polynomial) energy stability is achieved in an (exponential and polynomial) kernel function state.
PubDate: 2022-04-04

• Global existence and blowup of solutions for a semilinear Klein-Gordon
equation with the product of logarithmic and power-type nonlinearity

Abstract: Abstract In this paper we study the initial boundary value problem of a semilinear Klein-Gordon equation with the multiplication of logarithmic and polynomial nonlinearities. By using potential well method and energy method, we obtain the existence of global solutions and finite-time blowup solutions.
PubDate: 2022-04-04

• A note on the rearrangement of functions in time and on the parabolic
Talenti inequality

Abstract: Abstract Talenti inequalities are a central feature in the qualitative analysis of PDE constrained optimal control as well as in calculus of variations. The classical parabolic Talenti inequality states that if we consider the parabolic equation $${\frac{\partial u}{\partial t}}-\Delta u=f=f(t,x)$$ then, replacing, for any time t, $$f(t,\cdot )$$ with its Schwarz rearrangement $$f^\#(t,\cdot )$$ increases the concentration of the solution in the following sense: letting v be the solution of $${\frac{\partial v}{\partial t}}-\Delta v=f^\#$$ in the ball, then the solution u is less concentrated than v. This property can be rephrased in terms of the existence of a maximal element for a certain order relationship. It is natural to try and rearrange the source term not only in space but also in time, and thus to investigate the existence of such a maximal element when we rearrange the function with respect to the two variables. In the present paper we prove that this is not possible.
PubDate: 2022-03-23

• About well-posedness and lack of exponential stability of Shear beam
models

Abstract: Abstract In this paper, we consider the Shear beam model (no rotary inertia) and we stablished a decay result of the total energy of solutions by taking a feedback law acting on angle rotation. Unlike the dissipative Shear beam model with damping effect acting on vertical displacement, where the exponential decay holds irrespective any relationship between coefficients of the system, here we prove that system is non-exponential stability by using semigroup techniques. Also, the well-posedness is achieved by using semigroup theory.
PubDate: 2022-03-10
DOI: 10.1007/s11565-022-00391-z

• A note on non-uniform points for projections of hypersurfaces

Abstract: Abstract Let X be an irreducible, reduced complex projective hypersurface of degree d. A uniform point for X is a point P such that the projection of X from P has maximal monodromy. We extend and improve some results concerning the finiteness of the locus of non-uniform points for projections of hypersurfaces obtained by the authors and Cuzzucoli (Ann. Mat. Pura ed Appl. 1923, 1–18 (2021)) only for P not contained in X.
PubDate: 2022-02-27
DOI: 10.1007/s11565-022-00390-0

• On w-FI-flat and w-FI-injective modules

Abstract: Abstract In this paper, we generalize, with respect to the w-operation, the notions of FI-injective and FI-flat modules introduced by L. Mao and N. Ding. Let R be a ring. An R-module M is called w-FI-flat if $$\mathrm{Tor}_{1}^{R}(E,M)=0$$ for any absolutely w-pure R-module E, and M is said to be w-FI-injective if $$\mathrm{Ext}_{R}^{1}(E,M)=0$$ for any absolutely w-pure R-module E. The introduced modules are studied and compared with other classical modules. Among other things, we show that every module has a w-FI-flat cover. We use also the introduced modules to characterize some well known kind of rings.
PubDate: 2022-02-25
DOI: 10.1007/s11565-022-00388-8

• Time-smoothing for parabolic variational problems in metric measure spaces

Abstract: Abstract In 2013, Masson and Siljander determined a method to prove that the minimal p-weak upper gradient $$g_{f_\varepsilon }$$ for the time mollification $$f_\varepsilon$$ , $$\varepsilon >0$$ , of a parabolic Newton–Sobolev function $$f\in L^p_\mathrm {loc}(0,\tau ;N^{1,p}_\mathrm {loc}(\Omega ))$$ , with $$\tau >0$$ and $$\Omega$$ open domain in a doubling metric measure space $$(\mathbb {X},d,\mu )$$ supporting a weak (1, p)-Poincaré inequality, $$p\in (1,\infty )$$ , is such that $$g_{f-f_\varepsilon }\rightarrow 0$$ as $$\varepsilon \rightarrow 0$$ in $$L^p_\mathrm {loc}(\Omega _\tau )$$ , $$\Omega _\tau$$ being the parabolic cylinder $$\Omega _\tau :=\Omega \times (0,\tau )$$ . Their approach involved the use of Cheeger’s differential structure, and therefore exhibited some limitations; here, we shall see that the definition and the formal properties of the parabolic Sobolev spaces themselves allow to find a more direct method to show such convergence, which relies on p-weak upper gradients only and which is valid regardless of structural assumptions on the ambient space, also in the limiting case when $$p=1$$ .
PubDate: 2022-02-21
DOI: 10.1007/s11565-022-00389-7

• Correction to: Two algorithms for solving mixed equilibrium problems and
fixed point problems in Hilbert spaces

PubDate: 2022-02-07
DOI: 10.1007/s11565-022-00386-w

• Correction to: Generalization of Titchmarsh theorem in the deformed Hankel
setting

PubDate: 2022-02-03
DOI: 10.1007/s11565-022-00385-x

• Correction to: Strictly hyperbolic Cauchy problems on
$${\varvec{{\mathbb{R}}^n}}$$ R n with unbounded and singular coefficients

PubDate: 2022-02-02
DOI: 10.1007/s11565-022-00384-y

• Equivalence between K-functionals and modulus of smoothness on the
quaternion algebra

Abstract: Abstract In the space $$L^{2}({\mathbb {R}}^{2},{\mathcal {H}})$$ , using the analog of the Steklov operator, we construct the generalized modulus of smoothness, and also using the Laplacian operator we define the K-functional. The main result of our article is the proof of the equivalence between K-functionals and modulus of smoothness.
PubDate: 2022-01-29
DOI: 10.1007/s11565-022-00387-9

• Weak Hopfcity and singular modules

Abstract: Abstract The concept of Hopfian modules has been extensively studied in the literature. In this paper, we introduce and study the notion of $$\delta$$ -weakly Hopfian modules. The class of $$\delta$$ -weakly Hopfian modules lies properly between the class of Hopfian modules and the class of weakly Hopfian modules. It is shown that over a ring R, every quasi-projective R-module is $$\delta$$ -weakly Hopfian iff $$\delta (R)=J(R)$$ . We prove that any weak duo module, with zero radical is $$\delta$$ -weakly Hopfian. Let M be a module such that M satisfies ascending chain conditions on $$\delta$$ -small submodules. Then it is shown that M is $$\delta$$ -weakly Hopfian. Some other properties of $$\delta$$ -weakly Hopfian modules are also obtained with examples.
PubDate: 2022-01-08
DOI: 10.1007/s11565-021-00383-5

• Thermal convection with generalized friction

Abstract: Abstract A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the $$L^2$$ norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the $$L^{\beta +1}$$ norm for the perturbation temperature, where $$\beta >1$$ .
PubDate: 2021-12-17
DOI: 10.1007/s11565-021-00382-6

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