Annali dell''Universita di Ferrara最新文献

{"title":"Oskolkov-type constitutive heat models and Darcy convection","authors":"Brian Straughan","doi":"10.1007/s11565-026-00765-7","DOIUrl":"10.1007/s11565-026-00765-7","url":null,"abstract":"<div><p>We present general classes of constitutive equations for the heat flux in a Darcy porous medium. These heat models are based on rate type equations and the mathematical structure is analogous to the one introduced by Oskolkov in viscoelastic fluids. We focus attention on thermal convection when the heat flux is one of Kelvin–Voigt type and it is shown that this significantly changes the qualitative behaviour of Hopf bifurcation. Indeed, by considering different classes of heat flux one is able to produce a range of novel dynamical systems which undoubtedly will predict very interesting new behaviours for convective motion in a Darcy porous medium. The general heat flux models we introduce here are nominated as Cattaneo–Oskolkov theory, Jeffreys–Oskolkov theory, and Kelvin–Voigt–Oskolkov theory. These three classes display hyperbolic behaviour, qualitative behaviour which ranges from nearly hyperbolic to strongly damped, and strongly damped solutions.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On convolved weight matrices and local solvability with controlled loss of regularity","authors":"Gerhard Schindl","doi":"10.1007/s11565-026-00763-9","DOIUrl":"10.1007/s11565-026-00763-9","url":null,"abstract":"<div><p>We introduce the convolution between abstractly given anisotropic weight matrices and investigate properties of this new construction. Further, we apply the knowledge to the particular but interesting case when the (isotropic) matrices are associated with weight functions in the sense of Braun-Meise-Taylor and show how the convolution of associated weight matrices modifies the underlying weight functions. Finally, we give a concrete application of the convolution when studying the concept of local solvability for a certain hyperbolic PDE. Indeed, the convolution allows to treat in a natural way a mixed setting; i.e. having a controlled loss of regularity expressed in terms of two, in general different, weight sequences.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13623990/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149115872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semilinear damped wave equation on a compact Lie group with a non-autonomous forcing term","authors":"Wenhui Chen,&nbsp;Sandra Lucente,&nbsp;Alessandro Palmieri","doi":"10.1007/s11565-026-00764-8","DOIUrl":"10.1007/s11565-026-00764-8","url":null,"abstract":"<div><p>In the present note, we consider a semilinear damped wave equation on a compact Lie group with a non-autonomous nonlinearity <span>(varphi (t)|u|^p)</span>. We are interested in describing how the nonnegative time-dependent factor <span>(varphi )</span> affects the global in time prolongability of a local solution. In particular, the summability of the function <span>(varphi )</span> 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 <span>(varphi not in L^1([0,+infty )))</span> and satisfies a certain scaling condition, that we named uniform upper scaling condition.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00764-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On (q^2)-analogue of non-homogeneous heat equation","authors":"Irfan Ali,&nbsp;Michael Ruzhansky,&nbsp;Serikbol Shaimardan","doi":"10.1007/s11565-026-00762-w","DOIUrl":"10.1007/s11565-026-00762-w","url":null,"abstract":"<div><p>In this paper, we study two Cauchy problems of <span>(q^2)</span>-heat equation, i.e. the non-homogeneous <span>(q^2)</span>-heat equation and the inverse source problem of <span>(q^2)</span>-heat equation. We have used the <span>(q^2)</span>-Fourier transform and <i>q</i>-convolution techniques to find our solution. Specifically, we have constructed our <span>(q^2)</span>-heat equation with the combination of Jackson’s and Rubin’s <i>q</i>-derivative operators. Moreover, we find the solution by using the <span>(q^2)</span>-Fourier transform with <i>q</i>-convolution and obtain the well-posedness results on appropriate <i>q</i>-Sobolev type spaces.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Operational matrix formulation for linear difference equations using (nabla _lambda )-appell polynomial bases","authors":"Stiven Díaz,&nbsp;William Ramírez,&nbsp;Alejandro Urieles,&nbsp;Emiro Castaño","doi":"10.1007/s11565-026-00750-0","DOIUrl":"10.1007/s11565-026-00750-0","url":null,"abstract":"<div><p>This paper develops an operational matrix formulation for nonhomogeneous linear difference equations with constant coefficients in powers of the backward difference operator. Using general <span>(nabla _{lambda })</span>-Appell polynomial bases, the action of <span>(nabla _{lambda })</span> is represented algebraically on finite-dimensional Appell spaces, while the numerical approximation is obtained through finite expansions and collocation. Structural identities, change-of-basis matrices, Gram matrices and operational matrices are derived, allowing equations of the form </p><div><div><span>$$a_0y(x)+a_1nabla _{lambda }y(x)+cdots +a_mnabla _{lambda }^{m}y(x)=g(x)$$</span></div></div><p>to be reduced to finite-dimensional algebraic systems with initial or boundary conditions. Numerical examples with Bernoulli-type and Euler-type <span>(nabla _{lambda })</span>-Appell bases illustrate exact polynomial recovery, convergence for a non-polynomial test solution, and the influence of the chosen basis on conditioning.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00750-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Regularity criterion for the Navier–Stokes system with a cubic source term","authors":"Jishan Fan,&nbsp;Tohru Ozawa","doi":"10.1007/s11565-026-00761-x","DOIUrl":"10.1007/s11565-026-00761-x","url":null,"abstract":"<div><p>The regularity criterion of Kozono and Shimada is shown to apply to the <i>n</i> dimensional Navier–Stokes system with a cubic source term <span>(|u|^2u)</span> for <span>(n ge 2)</span>. A related conjecture is also proposed.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00761-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp anisotropic Gevrey regularization and directional microlocal smoothing for dissipative–dispersive Fourier evolutions","authors":"Alvaro H. Salas","doi":"10.1007/s11565-026-00757-7","DOIUrl":"10.1007/s11565-026-00757-7","url":null,"abstract":"<div><p>We establish a sharp Fourier–Gevrey regularization theory for a broad class of nonautonomous dissipative–dispersive evolution equations on <span>(mathbb {R}^n)</span>. The dissipative symbol is allowed to have different fractional orders in different coordinate directions, while the dispersive symbol is only required to be real. We prove an exact moving-radius estimate in exponentially weighted Fourier spaces: each anisotropic regularity radius increases by precisely the time integral of the corresponding dissipative coefficient. For the model symbol <span>(sum _j c_j(t)|xi _j|^{kappa _j})</span>, this threshold is optimal in every coordinate, in the strong sense that the evolution operator is bounded between two Fourier–Gevrey spaces if and only if the target radius does not exceed the initial radius plus the accumulated dissipation. Explicit factorial derivative estimates identify the sharp anisotropic Gevrey indices <span>(1/kappa _j)</span>, including analytic and ultra-analytic regimes. We also treat inhomogeneous problems and complex lower-order Fourier perturbations. In the microlocal part we develop a nonquasianalytic anisotropic formulation for mixed exponents <span>(0&lt;kappa _j&lt;1)</span>. Writing <span>(kappa _*=max _jkappa _j)</span>, <span>(q_j=kappa _*/kappa _j)</span>, and <span>(sigma =1/kappa _*)</span>, we use <span>(varvec{q})</span>-conic neighborhoods and the anisotropic Gevrey scale <span>(mathcal {G}^{sigma varvec{q}})</span>, in the spirit of Zanghirati’s anisotropic microlocal theory. If the integrated dissipation is elliptic only in a <span>(varvec{q})</span>-cone, we prove elimination of the corresponding anisotropic Gevrey singularities in every strictly smaller <span>(varvec{q})</span>-cone. We also show, for a time-dependent vector-field phase, that singularities in an undamped cone are transported by the characteristic translation rather than smoothed. Applications include fractional transport–diffusion, dissipative Schrödinger and Airy evolutions, mixed-order anisotropic models, cone-selective damping, and directional propagation.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00757-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fourier and microlocal methods for quantum Rabi systems","authors":"Marcello Malagutti,&nbsp;Alberto Parmeggiani","doi":"10.1007/s11565-026-00749-7","DOIUrl":"10.1007/s11565-026-00749-7","url":null,"abstract":"<div><p>We give a concise presentation two perturbative approaches to the spectral analysis of Quantum Rabi systems. For the one-mode two-level model, a metaplectic translation reduces the Hamiltonian to a bounded analytic perturbation of a doubled harmonic oscillator. The first-order effective matrix is computed by Fourier-Hermite methods and its entries are expressed through Laguerre polynomials. This gives analytic spectral branches, parity information, and the validity of Braak’s conjecture on arbitrary fixed finite spectral windows for a sufficiently small atomic gap. We also discuss multi-level, multi-mode Rabi systems, for <span>(n=2)</span> and <span>(N=3)</span>. Although their semiprincipal symbols need not be smoothly diagonalizable, an order-one regularizing perturbation places them in a globally diagonalizable class; comparison by the minimax principle then yields a two-term Weyl asymptotic formula. Complete proofs and additional computations appear in [12]; here the emphasis is on the Fourier and microlocal techniques behind the results.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13590440/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149017492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Time-dependent Kirchhoff–Pokhozhaev equations with conservation laws of all orders (ge 2)","authors":"Renato Manfrin","doi":"10.1007/s11565-026-00746-w","DOIUrl":"10.1007/s11565-026-00746-w","url":null,"abstract":"<div><p>We extend the results of [3, 4] for the Kirchhoff–Pokhozhaev equation to a class of quasilinear time-dependent Kirchhoff equations. For this class, we establish energy-type conservation laws of all orders <span>(ge 2)</span>.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the nontrapping condition and its role in the smoothing effect of dispersive operators","authors":"Serena Federico","doi":"10.1007/s11565-026-00760-y","DOIUrl":"10.1007/s11565-026-00760-y","url":null,"abstract":"<div><p>In this paper, we discuss the smoothing effect of some dispersive operators with variable coefficients in connection with the so called nontrapping condition (NTC). The operators under consideration are of order <span>(m=2,3)</span>, and we shall show that, in some cases, a global nontrapping property of an operator <span>(A(x,D_x))</span> leads to the local smoothing effect for the dispersive operator <span>(D_t-A(x,D_x))</span>. On the other hand, smallness assumptions on <span>(A(x,D_x))</span> imply the local smoothing effect without assuming the global nontrapping property. We shall start our exposition with some fundamental results on the microlocal smoothing effect of Schrödinger operators with variable coefficients, emphasizing the role of the nontrapping condition. Then, we will focus on the local smoothing, both homogeneous and inhomogeneous, of operators of order two and three with and without the nontrapping condition. This survey is based mainly on the results of the pioneering works [6, 11, 13, 14, 41] and of the recent paper [23].</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"72 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-026-00760-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148987037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}