1,720,994 research outputs found
A kinetic theory approach to the dynamics of crowd evacuation from bounded domains
Full text linkA mathematical model of the evacuation of a crowd from bounded domains is derived by a hybrid approach with kinetic and macro-features. Interactions at the micro-scale, which modify the velocity direction, are modeled by using tools of game theory and are transferred to the dynamics of collective behaviors. The velocity modulus is assumed to depend on the local density. The modeling approach considers dynamics caused by interactions of pedestrians not only with all the other pedestrians, but also with the geometry of the domain, such as walls and exits. Interactions with the boundary of the domain are non-local and described by games. Numerical simulations are developed to study evacuation time depending on the size of the exit zone, on the initial distribution of the crowd and on a parameter which weighs the unconscious attraction of the stream and the search for less crowded walking directions.Fil: Agnelli, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Colasuonno, F.. Politecnico di Torino; ItaliaFil: Knopoff, Damián Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin
)‐Laplacian problems
Full text linkWe investigate the existence and the multiplicity of solutions of the problem (Formula presented.) where Ω is a smooth, bounded domain of (Formula presented.), 1 < p < q < ∞, and the nonlinearity g behaves as uq − 1 at infinity. We use variational methods and find multiple solutions as minimax critical points of the associated energy functional. Under suitable assumptions on the nonlinearity, we cover also the resonant case
Symmetry and rigidity for the hinged composite plate problem
Full text linkThe composite plate problem is an eigenvalue optimization problem related to the fourth order operator (−Δ) 2 . In this paper we continue the study started in [10], focusing on symmetry and rigidity issues in the case of the hinged composite plate problem, a specific situation that allows us to exploit classical techniques like the moving plane method
Multiplicity of solutions for the Minkowski-curvature equation via shooting method
Full text linkIn this paper we prove the existence and the multiplicity of radial positive oscillatory solutions for a nonlinear problem governed by the mean curvature operator in the Lorentz-Minkowski space. The problem is set in an N-dimensional ball and is subject to Neumann boundary conditions. The main tool used is the shooting method for ODEs
Upper and Lower Motor Neurons and the Skeletal Muscle: Implication for Amyotrophic Lateral Sclerosis (ALS)
No full textThe relationships between motor neurons and the skeletal muscle during development and in pathologic contexts are addressed in this Chapter.We discuss the developmental interplay of muscle and nervous tissue, through neurotrophins and the activation of differentiation and survival pathways. After a brief overview on muscular regulatory factors, we focus on the contribution of muscle to early and late neurodevelopment. Such a role seems especially intriguing in relation to the epigenetic shaping of developing motor neuron fate choices. In this context, emphasis is attributed to factors regulating energy metabolism, which may concomitantly act in muscle and neural cells, being involved in common pathways.We then review the main features of motor neuron diseases, addressing the cellular processes underlying clinical symptoms. The involvement of different muscle-associated neurotrophic factors for survival of lateral motor column neurons, innervating MyoD-dependent limb muscles, and of medial motor column neurons, innervating Myf5-dependent back musculature is discussed. Among the pathogenic mechanisms, we focus on oxidative stress, that represents a common and early trait in several neurodegenerative disorders. The role of organelles primarily involved in reactive oxygen species scavenging and, more generally, in energy metabolism-namely mitochondria and peroxisomes-is discussed in the frame of motor neuron degeneration.We finally address muscular involvement in amyotrophic lateral sclerosis (ALS), a multifactorial degenerative disorder, hallmarked by severe weight loss, caused by imbalanced lipid metabolism. Even though multiple mechanisms have been recognized to play a role in the disease, current literature generally assumes that the primum movens is neuronal degeneration and that muscle atrophy is only a consequence of such pathogenic event. However, several lines of evidence point to the muscle as primarily involved in the disease, mainly through its role in energy homeostasis. Data from different ALS mouse models strongly argue for an early mitochondrial dysfunction in muscle tissue, possibly leading to motor neuron disturbances. Detailed understanding of skeletal muscle contribution to ALS pathogenesis will likely lead to the identification of novel therapeutic strategies
On the Born–Infeld equation for electrostatic fields with a superposition of point charges
No full textIn this paper, we study the static Born–Infeld equation -div(∇u1-|∇u|2)=∑k=1nakδxkinRN,lim|x|→∞u(x)=0,where N≥ 3 , ak∈ R for all k= 1 , ⋯ , n, xk∈ RN are the positions of the point charges, possibly non-symmetrically distributed, and δxk is the Dirac delta distribution centered at xk. For this problem, we give explicit quantitative sufficient conditions on ak and xk to guarantee that the minimizer of the energy functional associated with the problem solves the associated Euler–Lagrange equation. Furthermore, we provide a more rigorous proof of some previous results on the nature of the singularities of the minimizer at the points xk’s depending on the sign of charges ak’s. For every m∈ N, we also consider the approximated problem -∑h=1mαhΔ2hu=∑k=1nakδxkinRN,lim|x|→∞u(x)=0where the differential operator is replaced by its Taylor expansion of order 2m (see (2.1)). It is known that each of these problems has a unique solution. We study the regularity of the approximating solution, the nature of its singularities, and the asymptotic behavior of the solution and of its gradient near the singularities
A priori bounds and multiplicity of positive solutions for p-Laplacian Neumann problems with sub-critical growth
Full text linkLet 1 < p < +∞ and let Ω C RN be either a ball or an annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris, ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann problems of the type 0,rm in Ω ,quad partialν u = 0rm on Ω.]]>We suppose that f(0) = f(1) = 0 and that f is negative between the two zeros and positive after. In case Ω is a ball, we also require that f grows less than the Sobolev-critical power at infinity. We prove a priori bounds of radial solutions, focussing in particular on solutions which start above 1. As an application, we use the shooting technique to get existence, multiplicity and oscillatory behaviour (around 1) of non-constant radial solutions
A nonlocal supercritical Neumann problem
Full text linkWe establish existence of positive non-decreasing radial solutions for a
nonlocal nonlinear Neumann problem both in the ball and in the annulus. The
nonlinearity that we consider is rather general, allowing for supercritical
growth (in the sense of Sobolev embedding). The consequent lack of compactness
can be overcome, by working in the cone of non-negative and non-decreasing
radial functions. Within this cone, we establish some a priori estimates which
allow, via a truncation argument, to use variational methods for proving
existence of solutions. As a side result, we prove a strong maximum principle
for nonlocal Neumann problems, which is of independent interest.Comment: 32 pages, 0 figures. In version v2, two typos in Lemma 3.6 have been
fixed, with respect to the published versio
Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions
Full text linkWe analyze existence, multiplicity and oscillatory behavior of positive radial solutions to a class of quasilinear equations governed by the Lorentz-Minkowski mean curvature operator. The equation is set in a ball or an annulus of RN, is subject to homogeneous Neumann boundary conditions, and involves a nonlinear term on which we do not impose any growth condition at infinity. The main tool that we use is the shooting method for ODEs
Symmetry in the composite plate problem
Full text linkIn this paper, we deal with the composite plate problem, namely the following optimization eigenvalue problem: equation presented where P is a class of admissible densities, W = H 20 (Ω) for Dirichlet boundary conditions and W = H 2 (Ω) ∩ H 10 (Ω) for Navier boundary conditions. The associated Euler- Lagrange equation is a fourth-order elliptic PDE governed by the biharmonic operator Δ 2 . In the spirit of [S. Chanillo, D. Grieser, M. Imai, K. Kurata and I. Ohnishi, Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes, Comm. Math. Phys. 214 (2000) 315-337], we study qualitative properties of the optimal pairs (u, ρ). In particular, we prove existence and regularity and we find the explicit expression of ρ.When Ω is a ball, we can also prove uniqueness of the optimal pair, as well as positivity of u and radial symmetry of both u and ρ
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