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We study different notions of quasiconvexity for a subgroup $H$ of a relatively hyperbolic group $G.$ The first result establishes equivalent conditions for $H$ to be relatively quasiconvex. As a corollary we obtain that the relative…
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…
We devise a lucid and straightforward way for explicitly constructing quasi-periodic wave solutions (also called multi-periodic wave solutions) of supersymmetric equations in superspace $\mathbb{R}_\Lambda^{2,1}$ over two-dimensional…
We consider a second order non-autonomous system which can be interpreted as the Newtonian equation of motion on a Riemannian manifold under the action of time-quasiperiodic force field. The problem is to find conditions which ensures: (a)…
We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…
In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…
This letter addresses the question which, after a decade-long discussion, still remains open: what is the nature of the ultraquantum regime of decay of quantum turbulence? The model developed in this work reproduces both the ultraquantum…
Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…
This article concerns the formation of finite-time singularities in solutions to quasilinear hyperbolic systems with small initial data. By constructing a special test function, we first present a simpler proof of the main result in…
We investigate the electronic structure of twin boundaries in orthorhombically distorted high-T$_c$ materials using the quasiclassical theory of superconductivity. At low temperatures we find a local instability to a time-reversal symmetry…
In this paper, we establish a relation between two seemingly unrelated concepts for solving first-order hyperbolic quasilinear systems of partial differential equations in many dimensions. These concepts are based on a variant of the…
We study singularity formation in two one-dimensional nonlinear wave models with quadratic time-derivative nonlinearities. The non-null model violates the null condition and typically develops finite-time blow-up; the null-form model is…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power…
In this text, we shall give an outline of some recent results (see \ccite{bahourichemin2} \ccite{bahourichemin3} and \ccite{bahourichemin4}) of local wellposedness for two types of quasilinear wave equations for initial data less regular…
We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
A quasi-potential approximation to the Navier-Stokes equation for low viscosity fluids is developed to study pattern formation in parametric surface waves driven by a force that has two frequency components. A bicritical line separating…
Bound state in the continuum (BIC) and quasi-BIC represent a remarkable class of wave functions that disobey conventional intuition by exhibiting spatially localized modes embedded in the continuum spectrum. In recent years, these states…