A Liouville theorem for fully nonlinear problems with infinite **boundary**
**conditions** and applications

**boundary**blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions. Expand abstract.

**boundary**value problems related to fully nonlinear, uniformly elliptic operators. We then apply the result in order to obtain gradient

**boundary**blow up rates for ergodic functions in bounded domains related to degenerate/singular operators, and, as a further consequence, we deduce the uniqueness of the ergodic functions.

9/10 relevant

arXiv

**Boundary** **conditions** for dynamic wetting -- A mathematical analysis

**boundary**

**conditions**have to be compatible at the contact line in order to allow for regular solutions. Expand abstract.

**condition**introduces a non-integrable and therefore unphysical singularity into the model, various models to relax the singularity have been proposed. Many of the relaxation mechanisms still retain a weak (integrable) singularity, while other approaches look for completely regular solutions with finite curvature and pressure at the moving contact line. In particular, the model introduced recently in (Lukyanov, Pryer, Langmuir 2017) aims for regular solutions through modified

**boundary**

**conditions**. The present work applies the mathematical tool of compatibility analysis to continuum models of dynamic wetting. The basic idea is that the

**boundary**

**conditions**have to be compatible at the contact line in order to allow for regular solutions. Remarkably, the method allows to compute explicit expressions for the pressure and the curvature locally at the moving contact line for regular solutions to the model by Lukyanov and Pryer. It is found that the solution may still be singular for the latter model.

10/10 relevant

arXiv

Riemann-Hilbert approach and soliton solutions for the higher-order
dispersive nonlinear Schr\"{o}dinger equation with nonzero **boundary**
**conditions**

**boundary**

**conditions**at infinity is investigated including the simple and double zeros of the scattering coefficients. Expand abstract.

**boundary**

**conditions**at infinity is investigated including the simple and double zeros of the scattering coefficients. We introduce a appropriate Riemann surface and uniformization variable in order to deal with the double-valued functions occurring in the process of direct scattering. Then, the direct scattering problem is analyzed involving the analyticity, symmetries and asymptotic behaviors. Moreover, for the cases of simple and double poles, we study the discrete spectrum and residual conditions, trace foumulae and theta

**conditions**and the inverse scattering problem which is solved via the Riemann-Hilbert method. Finally, for the both cases, we construct the soliton and breather solutions under the

**condition**of reflection-less potentials. Some interesting phenomena of the soliton and breather solutions are analyzed graphically by considering the influences of each parameters.

9/10 relevant

arXiv

Annihilation-to-nothing: a quantum gravitational **boundary** **condition** for
the Schwarzschild black hole

5/10 relevant

arXiv

The nature of mean-field generation in three classes of optimal dynamos

**boundary**

**conditions**(where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Expand abstract.

**boundary**

**conditions**are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15% supercritical. When the mean magnetic field satisfies homogeneous

**boundary**

**conditions**(where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

5/10 relevant

arXiv

Concentrated reaction terms on the **boundary** of rough domains for a
quasilinear equation

**boundary**

**conditions**set in a family of rough domains with a nonlinear term concentrated on the

**boundary**. At the limit, we get a nonlinear

**boundary**

**condition**capturing the oscillatory geometry of the strip where the reactions take place.

8/10 relevant

arXiv

Riemann-Hilbert approach for the NLSLab equation with nonzero **boundary**
**conditions**

**boundary**

**conditions**(NZBCs) at infinity. In order to better deal with the scattering problem of NZBCs, we introduce the two-sheeted Riemann surface of $\kappa$, then it convert into the standard complex $z$-plane. In the direct scattering problem, we study the analyticity, symmetries and asymptotic behaviors of the Jost function and the scattering matrix in detail. In addition, we establish the discrete spectrum, residual conditions, trace foumulae and theta

**conditions**for the case of simple poles and double poles. The inverse problems of simple poles and double poles are from the Riemann-Hilbert problem (RHP). Finally, we obtain some soliton solutions of the NLSLab equation, including stationary solitons, non-stationary solitons and multi-soliton solutions. Some features of these soliton solutions caused by the influences of each parameters are analyzed graphically in order to control such nonlinear phenomena.

10/10 relevant

arXiv

Cut Bogner-Fox-Schmit Elements for Plates

**boundary**

**conditions**together with addition of certain stabilization terms that enable us to establish coercivity and stability of the resulting system of linear equations. We also take geometric approximation of the

**boundary**into account and we focus our presentation on the simply supported

**boundary**

**conditions**which is the most sensitive case for geometric approximation of the

**boundary**.

4/10 relevant

arXiv

**Boundary** **Conditions** and the q-state Potts model on Random Planar Maps

**boundary**. In this paper we explore the $(q

8/10 relevant

arXiv

Non-standard anomalous heat conduction in harmonic chains with correlated isotopic disorder

**boundary**conditions, whereas for fixed

**boundary**

**conditions**$\kappa \sim N^{(\beta-1)/(2+\beta)}$; where $\beta>-1$, which is the usual power law scaling for one dimensional systems. Nevertheless, if $W$ does not scale as a power law in the low wavelength limit, the thermal conductivity may not scale in its usual form $\kappa\sim N^{\alpha}$, where the value of $\alpha$ depends on the particular one dimensional model. As an example of the latter statement, if $W(\mu)\sim \exp(-1/\mu)/\mu^2$, $\kappa \sim N/(\log N)^3$ for fixed

**boundary**

**conditions**and $\kappa \sim N/\log(N)$ for free

**boundary**conditions, which represent non-standard scalings of the thermal conductivity.

5/10 relevant

arXiv