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We study the initial-boundary value problem for the Fokker-Planck equation in an interval with absorbing boundary conditions. We develop a theory of well-posedness of classical solutions for the problem. We also prove that the resulting…

This work intends to prove that strong instabilities may appear for high order geometric optics expansions of weakly stable quasilinear hyperbolic boundary value problems, when the forcing boundary term is perturbed by a small amplitude…

We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial spacelike hypersurface with a timelike boundary, there exists a unique, local in time solution to the Einstein equations in a…

We present a new approach for boundary integral equations for the wave equation with zero initial conditions. Unlike previous attempts, our mathematical formulation allows us to prove that the associated boundary integral operators are…

We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…

In this paper, we study the partial data inverse boundary value problem for the Schrodinger operator at a high frequency k>=1 in a bounded domain with smooth boundary in Rn, n>=3. Assuming that the potential is known in a neighborhood of…

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…

We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem

The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…

Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…

We study static, spherically symmetric, self-gravitating systems minimally coupled to a scalar field with U(1) gauge symmetry: charged boson stars. We find numerical solutions to the EinsteinMaxwell equations coupled to the relativistic…

We study the well-posedness of the initial value (Cauchy) problem of vacuum Einstein-aether theory. The latter is a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical timelike 'aether' vector field,…

In this article we summarize what is known about the initial-boundary value problem for general relativity and discuss present problems related to it.

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a…

In this paper, complex Ginzburg-Landau (CGL) equations governed by p-Laplacian are studied. We discuss the global existence of solutions for the initial-boundary value problem of the equation in general domains. The global solvability of…

The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the…

Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum Einstein spacetimes with T2 symmetry, establish the global well-posedness of the initial value problem for Einstein's field equations, and investigate…

This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $\Omega…

We argue that our recent success in using our resummed quantum gravity approach to Einstein's general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the…