Browsing by Author "Roman, Carlos"

Now showing 1 - 3 of 3
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    Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem
    (2023) Roman, Carlos; Sandier, Etienne; Serfaty, Sylvia
    We consider the full three-dimensional Ginzburg-Landau model of superconductivity with applied magnetic field, in the regime where the intensity of the applied field is close to the 'first critical field' Hc1$H_{c_1}$ at which vortex filaments appear, and in the asymptotics of a small inverse Ginzburg-Landau parameter epsilon$\varepsilon$. This onset of vorticity is directly related to an 'isoflux problem' on curves (finding a curve that maximizes the ratio of a magnetic flux by its length), whose study was initiated in [22] and which we continue here. By assuming a nondegeneracy condition for this isoflux problem, which we show holds at least for instance in the case of a ball, we prove that if the intensity of the applied field remains below Hc1+Clog|log epsilon|${H_{c_1}}+ C \log {|\log \varepsilon |}$, the total vorticity remains bounded independently of epsilon$\varepsilon$, with vortex lines concentrating near the maximizer of the isoflux problem, thus extending to the three-dimensional setting a two-dimensional result of [28]. We finish by showing an improved estimate on the value of Hc1${H_{c_1}}$ in some specific simple geometries.
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    Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3
    (2019) del Pino, Manuel; Musso, Monica; Roman, Carlos; Wei, Juncheng
    We consider the problem of finding positive solutions of the problem u -.u + u5 = 0 in a bounded, smooth domain in R3, under zero Neumann boundary conditions. Here. is a positive number. We analyze the role of Green's function of - +. in the presence of solutions exhibiting single bubbling behavior at one point of the domain when. is regarded as a parameter. As a special case of our results, we find and characterize a positive value.* such that if. -. * > 0 is sufficiently small, then this problem is solvable by a solution u. which blows-up by bubbling at a certain interior point of lambda down arrow lambda(*).
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    Unbounded mass radial solutions for the Keller-Segel equation in the disk
    (SPRINGER HEIDELBERG, 2021) Bonheure, Denis; Casteras, Jean Baptiste; Roman, Carlos
    We consider the boundary value problem