Related papers: Symmetric solutions of evolutionary partial differ…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
We investigate slowly converging solutions for non-linear evolution equations of elliptic or parabolic type. These equations arise from the study of isolated singularities in geometric variational problems. Slowly converging solutions have…
By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
We present easily verifiable sufficient conditions of time-independence and commutativity for local and nonlocal symmetries for a large class of homogeneous (1+1)-dimensional evolution systems. In contrast with the majority of known…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
The constraint equations for smooth $[n+1]$-dimensional (with $n\geq 3$) Riemannian or Lorentzian spaces satisfying the Einstein field equations are considered. It is shown, regardless of the signature of the primary space, that the…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
This paper recalls some classical motivations in fluid dynamics leading to a partial differential equation which is prescribed on a domain whose boundary possesses two connected components, one endowed with a Dirichlet datum, and the other…
We consider stable solutions of a semilinear elliptic equation with homogeneous Neumann boundary conditions. A classical result of Casten, Holland [20] and Matano [44] states that all stable solutions are constant in convex bounded domains.…
The dynamical systems methods are used to study evolution of the polymerised scalar field cosmologies with the cosmological constant. We have found all evolutional paths admissible for all initial conditions on the two-dimensional phase…
We consider an integral equation in the plane, in which the leading operator is of convolution type, and we prove that monotone (or stable) solutions are necessarily one-dimensional.
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
The issue of symmetry and symmetry breaking is fundamental in all areas of science. Symmetry is often assimilated to order and beauty while symmetry breaking is the source of many interesting phenomena such as phase transitions,…
We consider the Dirichlet problem for the nonlinear $p(x)$-Laplacian equation. For axially symmetric domains we prove that, under suitable assumptions, there exist Mountain-pass solutions which exhibit partial symmetry. Furthermore, we show…
In most fluid dynamics problems, the governing equations are nonlinear because of the presence of convective terms. Nevertheless, existence of solutions can be shown by direct sum provided one identifies, in the relevant Banach space of…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
The resolution of a very large class of linear and non-linear, stationary and evolutive partial differential problems in the half-space (or similar) under the slip boundary condition is reduced here to that of the corresponding results for…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…