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Titlebook: Nonlinear Differential Equations and Applications; Portugal-Italy Confe Hugo Beirão da Veiga,Feliz Minhós,Luís Sanchez Rod Conference proce

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Nonlinear Differential Equations and Applications978-3-031-53740-0Series ISSN 2364-950X Series E-ISSN 2364-9518
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The Kernel of the Strain Tensor for Solenoidal Vector Fields with Homogeneous Normal Trace,the maximal kernel dimension is achieved for balls. We also exhibit some nonsmooth domains for which the kernel is nontrivial. Finally, we introduce a related Stokes eigenvalue problem, and we discuss the relationship between our results and the classical Faber–Krahn inequality.
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Long-Time Behaviour for Solutions of Systems of PDEs Modelling Suspension Bridges,e energy is bounded by a quadratic function of time. The exploited technique relies on direct estimates of suitable energy functionals associated with the considered problem. The results are complemented by some numerical experiments.
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,Navier–Stokes Equations with Regularized Directional Boundary Condition,e Navier–Stokes equations with RDDN condition, under appropriate assumptions on the size of the data, which, however, are less restrictive when compared with the case of a CDN outflow condition. We present numerical experiments that illustrate the advantages of using the DDN and RDDN boundary conditions.
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Quantitative Study of the Stabilization Parameter in the Virtual Element Method,f a particular function in the discrete space, commonly known as the “hourglass mode.” Through this approach, this study sheds light on how the virtual element solution depends on the stabilization term, providing insights into the behavior of the method in more general scenarios.
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On the Existence and Stability of 2, Compressible Current-Vortex Sheets,sh–Moser iteration, provided the stability condition is satisfied at each point of the initial discontinuity..This survey paper presents our recent results in Morando et al. (Arch. Rational Mech. Anal. ., 50 (2023)).
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