Related papers: On Non-Autonomous Integro-Differential-Algebraic E…
Evolutionary processes proved very useful for solving optimization problems. In this work, we build a formalization of the notion of cooperation and competition of multiple systems working toward a common optimization goal of the population…
We discuss linear autonomous evolution equations on function spaces which have the property that a positive initial value leads to a solution which initially changes sign, but then becomes - and stays - positive again for sufficiently large…
We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Under suitable decay assumptions for $|x| \to \infty$ on these…
This paper is addressed to the well-posedness of some linear and semilinear backward stochastic differential equations with general filtration, without using the Martingale Representation Theorem. The point of our approach is to introduce a…
We study the well-posedness of nonautonomous nonlinear delay equations in $\mathbb{R}^{n}$ as evolutionary equations in a proper Hilbert space. We present a construction of solving operators (nonautonomous case) or nonlinear semigroups…
Despite the strong focus of regularization on ill-posed problems, the general construction of such methods has not been fully explored. Moreover, many previous studies cannot be clearly adapted to handle more complex scenarios, albeit the…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
We propose a new method for solution of the integrability problem for evolutionary differential-difference equations of arbitrary order. It enables us to produce necessary integrability conditions, to determine whether a given equation is…
We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator $\mathbf{T}$ that is singular of order $r_0\in[0,2]$. For $r_0\in(0,1]$ we prove well-posedness in Gevrey spaces $G^s$ with…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
In this paper, we investigate the well-posedness and asymptotic behavior of difference equations of the form $x(t) = A x(t - \tau(t))$, $t \geq 0$, where the unknown function $x$ takes values in $\mathbb R^d$ for some positive integer $d$,…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.
We study a nonlinear fourth-order extension of Richards' equation that describes infiltration processes in unsaturated soils. We prove the well-posedness of the fourth-order equation by first applying Kirchhoff's transformation to linearize…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
A straightforward algorithm for the symbolic computation of higher-order symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the…
We establish well-posedness results for multidimensional non degenerate $\alpha$-stable driven SDEs with time inhomogeneous singular drifts in $\mathbb{L}^r-{\mathbb B}_{p,q}^{-1+\gamma}$ with $\gamma<1$ and $\alpha$ in $(1,2]$, where…
Based on a combination of insights afforded by Rainer Picard and Serge Nicaise, we extend a set of abstract piezo-electromagnetic impedance boundary conditions. We achieve this by accommodating for the influence of heat with the inclusion…
We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…
In the article we establish the global well-posedness in W^{1, 2, 2}(R\times R^{+}) of the integro-differential equation in the case of the anomalous diffusion when the one dimensional negative Laplace operator is raised to a fractional…