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We introduce a one-dimensional, hyperbolic model for non-Newtonian fluids with finite relaxation time, derived within the framework of Rational Extended Thermodynamics (RET). Unlike classical parabolic models, our formulation preserves…
The Dirichlet-Neumann method is a common domain decomposition method for nonoverlapping domain decomposition and the method has been studied extensively for linear elliptic equations. However, for nonlinear elliptic equations, there are…
We extend classical results by Lavrent'ev and Kufarev concerning the product of the conformal radii of planar non-overlapping domains. We also extend relatively recent results for the case of domains in the $n$-dimensional Euclidean space,…
This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the…
We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of…
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…
In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…
We develop hybrid projection methods for computing solutions to large-scale inverse problems, where the solution represents a sum of different stochastic components. Such scenarios arise in many imaging applications (e.g., anomaly detection…
We study well-posedness of degenerate mixed-type parabolic-hyperbolic equations $$ \partial_tu+\textrm{div}\big(f(u)\big)=\mathcal{L}[b(u)] $$ on bounded domains with general Dirichlet boundary/exterior conditions. The nonlocal diffusion…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
We use the author's previous work on atomic decompositions of Besov spaces with spectrum on symmetric cones, to derive new atomic decompositions for Bergman spaces on tube type domains. It is related to work by Ricci and Taibleson who…
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of…
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
In the present paper we develop the general theory of renormalization of some nonequilibrium diagram technique. This technique roughly is the Keldysh diagram technique. To develop our theory we have used the Bogoliubov -Parasiuk R -…
We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…
We give a sufficient condition on the hyperplanes used in the inbreeding construction of Belolipetsky-Thomson to obtain nonarithmetic manifolds. We construct explicitly infinitely many examples of such manifolds that are pairwise…
In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and…
Alternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such…