Evolution problems associated with nonconvex closed moving sets with bounded variation.
Evolutionary Games in Space
The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop...
Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials.
Exact boundary controllability for higher order nonlinear Schrödinger equations with constant coefficients.
Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case
This paper is concerned with the global exact controllability of the semilinear heat equation (with nonlinear terms involving the state and the gradient) completed with boundary conditions of the form . We consider distributed controls, with support in a small set. The null controllability of similar linear systems has been analyzed in a previous first part of this work. In this second part we show that, when the nonlinear terms are locally Lipschitz-continuous and slightly superlinear, one...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients
The results of this paper concern exact controllability to the trajectories for a coupled system of semilinear heat equations. We have transmission conditions on the interface and Dirichlet boundary conditions at the external part of the boundary so that the system can be viewed as a single equation with discontinuous coefficients in the principal part. Exact controllability to the trajectories is proved when we consider distributed controls supported in the part of the domain where the diffusion...
Exact linear lumping in abstract spaces.
Exact null internal controllability for the heat equation on unbounded convex domains
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...
Exact solutions to some nonlinear PDEs, travelling profiles method.
Exceptional sets for solutions to quasilinear parabolic equations in weighted Sobolev spaces.
Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces.
Existence and asymptotic behaviour of positive solutions for some nonlinear parabolic systems in the half-space.
Existence and Asymptotic Behaviour of Solutions in a System of Reaction Diffusion Equations.
Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²
We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.
Existence and attractivity results for a class of degenerate functional-parabolic problems
Existence and attractors of solutions for nonlinear parabolic systems.
Existence and comparison results for quasilinear evolution hemivariational inequalities.