Related papers: On uniqueness for the Harmonic Map Heat Flow in su…
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with a special emphasis on phase transitions. We use ideas from…
We analyse finite-time singularities of the Teichm\"uller harmonic map flow -- a natural gradient flow of the harmonic map energy -- and find a canonical way of flowing beyond them in order to construct global solutions in full generality.…
We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…
In this paper we prove the existence of weak solutions for a thermodynamically consistent phase-field model introduced in [26] in two and three dimensions of space. We use a notion of solution inspired by [18], where the pointwise internal…
Existence and uniqueness of global in time measure solution for a one dimensional nonlinear aggregation equation is considered. Such a system can be written as a conservation law with a velocity field computed through a selfconsistant…
In this paper, we investigate the stratification theory for ``suitable solutions" of harmonic map flows based on the spatial symmetry of tangent measures. Generally, suitable solutions are a category of solutions that satisfy both the…
In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ${\mathbb R} \times {\mathbb R}^d$ with $d \geq 6$. We prove the stability of solutions under the weak condition…
This work contributes to an understanding of the domain size's effect on the existence and uniqueness of the linear convection--diffusion equation with integral-type boundary conditions, where boundary conditions depend non-locally on…
Consider a strictly hyperbolic $n\times n$ system of conservation laws, where each characteristic field is either genuinely nonlinear or linearly degenerate. In this standard setting, it is well known that there exists a Lipschitz semigroup…
We investigate the thermal responses of a harmonic oscillator chain coupled at its boundaries to heat baths held at different temperatures. This setup sustains a steady energy flux, continuously dissipating heat into both reservoirs. By…
This paper defines a parabolic frequency for solutions of the heat equation on a Ricci flow and proves it's monotonicity along the flow. Frequency monotonicity is known to have many useful consequences; here it is shown to provide a simple…
We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we…
We numerically benchmark methods for computing harmonic maps into the unit sphere, with particular focus on harmonic maps with singularities. For the discretization we compare two different approaches, both based on Lagrange finite…
In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…
Harmonic maps are nonlinear extensions of harmonic functions. They are critical points of natural energy functionals between Riemannian manifolds. Such type of problems appear in Physics, Geometry of Finance and the study of regularity and…
Heat losses through the building envelope is one of the key factors in the calculation of the building energy balance. If steady-state heat conduction is observed, which is commonly used to assess the heat losses in building, there is an…
Let $\Sigma$ be a compact oriented surface and $N$ a compact K\"ahler manifold with nonnegative holomorphic bisectional curvature. For a solution of harmonic map flow starting from an almost-holomorphic map $\Sigma \to N$ (in the energy…
We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…
An interesting observation is that most pairs of weakly homogeneous mappings have no strongly monotonic property, which is one of the key conditions to ensure the unique solvability of the generalized variational inequality. This paper…
We study the dynamics of phase relaxation between a pair of one-dimensional condensates created by a bi-directional, supersonic `unzipping' of a finite single condensate. We find that the system fractures into different \emph{extensive}…