Related papers: Three-Scale Singular Limits of Evolutionary PDEs
The properties of nonlinear PDEs that generate filtered solutions are explored with particular attention given to the constraints on the residual term. The analysis is carried out for nonlinear PDEs with an emphasis on evolution problems…
We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
The problem of partial null controllability for linear autonomous evolution equations, which are controlled by a one-dimensional control, is under consideration. The partial null-controllability conditions for coupled abstract evolution…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
We use partial differential equations (PDEs) to describe physical systems. In general, these equations include evolution and constraint equations. One method used to find solutions to these equations is the Free-evolution approach, which…
The evolution of dispersal rate is studied with a model of several local populations linked by dispersal. Three dispersal strategies are considered where all, half, or none of the offspring disperse. The spatial scale (number of patches)…
Many equations that model fluid behaviour are derived from systems that encompass multiple physical forces. When the equations are written in non dimensional form appropriate to the physics of the situation, the resulting partial…
We consider a class of stochastic kinetic equations, depending on two time scale separation parameters $\epsilon$ and $\delta$: the evolution equation contains singular terms with respect to $\epsilon$, and is driven by a fast ergodic…
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…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of…
We study initial boundary value problems for linear evolution partial differential equations (PDEs) posed on a time-dependent interval $l_1(t)<x<l_2(t)$, $0<t<T$, where $l_1(t)$ and $l_2(t)$ are given, real, differentiable functions, and…
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.
We consider a linear equation $\partial_t u = \mathcal{L}u$, where $\mathcal{L}$ is a generator of a semigroup of linear operators on a certain Hilbert space related to an initial condition $u(0)$ being a generalised stationary random field…
The short pulse equation (SPE) is considered as an initial-boundary value problem. It is found that the solutions of the SPE must satisfy an integral relation otherwise the temporal derivative exhibits discontinuities. This integral…
We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…
We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise…
Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.