Related papers: On four-dimensional Goursat problem in the non-cla…

We consider surfaces of constant Gaussian curvature immersed in 3-dimensional manifolds, and we strengthen the compactness result of Labourie in the case where the ambient manifold is 3-dimensional hyperbolic space. This allows us to prove…

In present paper we study a boundary value problem for a mixed parabolic-hyperbolic type equation in a rectangular domain and prove the existence of unique solution of this problem. In theory of boundary value problems for second order…

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

We give solutions to several decision problems in word hyperbolic groups

We deal, for the classical $N$-body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic,…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

We investigate degenerate cross-diffusion equations with a rank-deficient diffusion matrix that are considered to model populations which move as to avoid spatial crowding and have recently been found to arise in a mean-field limit of…

The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…

In the paper we present a functional-discrete method for solving the Goursat problem for nonlinear Klein-Gordon equation. The sufficient conditions providing that the proposed method converges superexponentially are obtained. The results of…

We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of the special form (Minkowski plane with a handle) containing closed timelike curves (time machines). We prove that the classical solution of the…

A classical problem in Complex Dynamics on hyperbolic domains is to characterize the hyperbolic step of parabolic functions. This topic has been studied by several authors, leading to different results and providing characterizations that…

A nonlinear parabolic equation of the fourth order is analyzed. The equation is characterized by a mobility coefficient that degenerates at 0. Existence of at least one weak solution is proved by using a regularization procedure and…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

We review curvature-based hyperbolic forms of the evolution part of the Cauchy problem of General Relativity that we have obtained recently. We emphasize first order symmetrizable hyperbolic systems possessing only physical characteristics.

We construct an example of a one-dimensional parabolic integro-differential equation with nonlocal diffusion which does not have asymptotically finite-dimensional dynamics in the corresponding state space. This example is more natural in…

We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, where the exponent satisfies the doubling condition. In particular, both the so called logconvex and…

We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We…

In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…

We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a result has previously been studied only for certain…