Related papers: Periodic solutions for implicit evolution inclusio…
In this work, an $r$-linearly converging adaptive solver is constructed for parabolic evolution equations in a simultaneous space-time variational formulation. Exploiting the product structure of the space-time cylinder, the family of trial…
We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…
We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of…
The paper is dedicated to a system of matrix nonlinear evolution equations related to a Hermitian symmetric space of the type $\mathbf{A.III}$. The system under consideration extends the $1+1$ dimensional Heisenberg ferromagnet equation in…
This paper addresses a doubly nonlinear parabolic inclusion of the form $A(u_t)+B(u)\ni f$. Existence of a solution is proved under suitable monotonicity, coercivity, and structure assumptions on the operators $A$ and $B$, which in…
This is a habilitation self-report describing results on forced periodic solutions of partial differential equations. Here averaging principle in the spirit of Bogoliubov and Mitropolsky for ODE's and Henry for parabolic equations are used…
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 study the cubic Szeg\"o equation which is an integrable nonlinear non-dispersive and nonlocal evolution equation. In particular, we present a direct approach for obtaining the multiphase and multisoliton solutions as well as a special…
The aim is to study the periodic solution problem for neutral evolution equation $$(u(t)-G(t,u(t-\xi)))'+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R$$in Banach space $X$, where $A:D(A)\subset X\rightarrow X$ is a closed linear operator, and…
In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…
In this paper, we consider evolution problems involving time dependent maximal monotone operators in Hilbert spaces. Existence and relaxation theorems are proved.
This article presents the convergence analysis of a sequence of piecewise constant and piecewise linear functions obtained by the Rothe method to the solution of the first order evolution partial differential inclusion…
We study the general properties of spectral curves associated to doubly-periodic solutions of Korteweg-deVries, sine-Gordon, Non-linear Schr\"odinger and 1D Toda equations, and construct examples of arbitrary genus.
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple quantized representation of these equations and their soliton solutions over a Fock space of bosons or of fermions. The classical…
This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an $n$-dimensional ball. By combining the variational methods and saddle point reduction technique, we prove there exist at least…
We study a third order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed,…
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x_0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We…