On the behavior of the free boundary for a one-phase Bernoulli problem
with mixed **boundary** **conditions**

**boundary**for a class of solutions to a one-phase Bernoulli free

**boundary**problem with mixed periodic-Dirichlet

**boundary**

**conditions**. It is shown that if the free

**boundary**of a symmetric local minimizer approaches the point where the two different

**conditions**meet, then it must do so at an angle of $\pi/2$

10/10 relevant

arXiv

Charged Dirac perturbations on Reissner-Nordstr\"om-Anti-de Sitter
spacetimes: quasinormal modes with Robin **boundary** **conditions**

**boundary**

**conditions**, as a generic principle, are applicable not only to neutral but also to electrically charged fields. Expand abstract.

**boundary**conditions, by extending our earlier work of neutral Dirac QNMs on Schwarzschild-AdS black holes. We first derive the equations of motion for charged Dirac fields on a RN-AdS background. To solve these equations we impose a requirement on the Dirac field: that its energy flux should vanish at asymptotic infinity. A set of two Robin

**boundary**

**conditions**compatible with QNMs is consequently found. By employing both analytic and numeric methods, we then obtain the quasinormal spectrum for charged Dirac fields, and analyse the impact of various parameters, in particular of electric charge. An analytic calculation shows explicitly that the charge coupling between the black hole and the Dirac field does not trigger superradiant instabilities. Numeric calculations, on the other hand, show quantiatively that Dirac QNMs may change substantially due to the electric charge. Our results illustrate how vanishing energy flux

**boundary**conditions, as a generic principle, are applicable not only to neutral but also to electrically charged fields.

10/10 relevant

arXiv

Inverse scattering transform and soliton solutions for the focusing
Kundu-Eckhaus equation with nonvanishing **boundary** **conditions**

**boundary**

**conditions**at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH) problem. Expand abstract.

**boundary**

**conditions**at infinity, under two cases: simple zeros and double zeros, is investigated systematically via Riemann-Hilbert (RH) problem. We derive some new results for the equation including the following seven parts. (I) The analyticities and symmetries of the Jost function and the scattering matrix are analyzed with the help of the normalized Lax pair. (II) Based on the resulting symmetries, the corresponding discrete spectrum set and residue

**conditions**of scattering coefficients are further obtained, which is very important to construct the formulae of solution to the original equation. (III) A generalized RH problem is established by combining the analytic properties of Jost functions and modified eigenfunctions. (IV) The RH problem is solved by the corresponding asymptotic behavior combined with the Plemelj's formulae and Cauchy operator. The expression of the solution to the focusing KE equation is given under the

**condition**of non-reflection. (V) From the reflection coefficients and discrete spectrums, the trace formula and the corresponding theta

**condition**are given to obtain the phase difference of the initial value at the

**boundary**. (VI) For the double zeros, there is a similar framework from the set of discrete spectral points, but the operation process is much more complicated than that of simple zeros, and new results and phenomena appear. (VII) Some interesting phenomena are obtained that one of the solutions is gradually to rouge waves when the spectrum points tend to singular points by choosing appropriate parameters.

10/10 relevant

arXiv

On the **Boundary** **Conditions** of Avoidance Memory Reconsolidation: An Attractor Network Perspective

**boundary**

**conditions**that can be tested experimentally. Expand abstract.

**boundary**

**conditions**have been extensively studied. Knowing their network mechanisms may lead to the development of better strategies for the treatment of fear and anxiety-related disorders. In 2011, Osan et al. developed a computational model for exploring such phenomena based on attractor dynamics, Hebbian plasticity and synaptic degradation induced by prediction error. This model was able to explain, in a single formalism, experimental findings regarding the freezing behavior of rodents submitted to contextual fear conditioning. In 2017, through the study of inhibitory avoidance in rats, Radiske et al. showed that the previous knowledge of a context as non-aversive is a

**boundary**

**condition**for the reconsolidation of the shock memory subsequently experienced in that context. In the present work, by adapting the model of Osan et al. (2011) to simulate the experimental protocols of Radiske et al. (2017), we show that such

**boundary**

**condition**is compatible with the dynamics of an attractor network that supports synaptic labilization common to reconsolidation and extinction. Additionally, by varying parameters such as the levels of protein synthesis and degradation, we predict behavioral outcomes, and thus

**boundary**

**conditions**that can be tested experimentally.

10/10 relevant

bioRxiv

Separation property and convergence to equilibrium for the equation and
dynamic **boundary** **condition** of Cahn-Hilliard type with singular potential

**boundary**

**conditions**and the total mass, in the bulk and on the boundary, is conserved for all time. Expand abstract.

**boundary**interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic type

**boundary**

**conditions**and the total mass, in the bulk and on the boundary, is conserved for all time. For the case with physically relevant singular (e.g., logarithmic) potential, global regularity of weak solutions is established. In particular, when the spatial dimension is two, we show the instantaneous strict separation property such that for arbitrary positive time any weak solution stays away from the pure phases +1 and -1, while in the three dimensional case, an eventual separation property for large time is obtained. As a consequence, we prove that every global weak solution converges to a single equilibrium as the time goes to infinity, by the usage of an extended Lojasiewicz-Simon inequality.

8/10 relevant

arXiv

The 3D inviscid limit problem with data analytic near the **boundary**

**boundary**

**conditions**in the horizontal directions. We prove the inviscid limit holds in the topology $L^\infty([0, T]; L^2(\mathbb H^3_+))$ assuming the initial datum is analytic in the region $\{(x, y, z)\in\mathbb H^3_+: 0\le z\le 1+\mu_0\}$ for some positive $\mu_0$ and has Sobolev regularity in the complement.

4/10 relevant

arXiv

Numerical simulation of the viral entry into a cell driven by the receptor diffusion

**boundary**

**conditions**. Expand abstract.

**boundary**

**conditions**. The first

**boundary**

**condition**states that the conservation of binders expressed as the local rate of change of density has to be equal to the negative of the local flux divergence. The second

**boundary**

**condition**represents the energy balance

**condition**with contributions due to the binding of receptors, the free energy of the membrane, its curvature and the kinetic energy due to the motion of the front. The described moving

**boundary**problem in terms of the binder density and the velocity of the adhesion front is well posed and relies on biomechanically motivated assumptions. The problem is numerically solved by using the finite difference method, and the illustrative examples have been chosen to show the influence of the mobility of the receptors and of their initial densities on the velocity of the process.

7/10 relevant

bioRxiv

Null-controllability of linear hyperbolic systems in one dimensional space

**boundary**

**conditions**on the other side, we previously established the optimal time for the null and the exact controllability for this system for a generic source term. Expand abstract.

**boundary**controls on one side. Under precise and generic assumptions on the

**boundary**

**conditions**on the other side, we previously established the optimal time for the null and the exact controllability for this system for a generic source term. In this work, we prove the null-controllability for any time greater than the optimal time and for any source term. Similar results for the exact controllability are also discussed.

4/10 relevant

arXiv

Asymptotic analysis of an optimal control problem for a viscous
incompressible fluid with Navier slip **boundary** **conditions**

**boundary**

**conditions**. We denote by $\alpha$ the friction coefficient and we analyze the asymptotic behavior of such a problem as $\alpha\to \infty$. More precisely, we prove that if we take an optimal control for each $\alpha$, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier-Stokes system with the Dirichlet

**boundary**

**condition**. We also show the convergence of the corresponding direct and adjoint states.

10/10 relevant

arXiv

On Fredholm **boundary** **conditions** on manifolds with corners I: Global
corner's cycles obstructions

7/10 relevant

arXiv