Related papers: Volterra Equations of the First kind with Disconti…
In this paper, we investigate and analyze numerical solutions for the Volterra integrodifferential equations with tempered multi-term kernels. Firstly we derive some regularity estimates of the exact solution. Then a temporal-discrete…
We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an…
Numerical solution of nonlocal constrained value problems with integrable kernels are considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed…
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…
This work studies a class of singular Volterra integral equations that are (controlled) and can be applied to memory-related problems.For optimum controls, we prove a second-order Pontryagin type maximal principle.
We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls…
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical…
Here an original idea is suggested to prove the existence of optimal control for some types of non- linear problems. The obtained results can be considered as individual existence theorems (in some sense).
A hyperbolic type integro-differential equation with two weakly singular kernels is considered together with mixed homogeneous Dirichlet and non-homogeneous Neumann boundary conditions. Existence and uniqueness of the solution is proved by…
Let $A$ be a densely defined closed, linear $\omega$-sectorial operator of angle $\theta\in [0,\frac{\pi}{2})$ on a Banach space $X$ for some $\omega\in\mathbb R$. We give an explicit representation (in terms of some special functions) and…
A universal kernel is constructed whose sections approximate any causal and time-invariant filter in the fading memory category with inputs and outputs in a finite-dimensional Euclidean space. This kernel is built using the reservoir…
A concise overview of the spectral theory of integral-functional operators is provided. In the context of analysis, a technique is described for deriving solutions to equations involving operators in a closed form. A constructive theorem…
The solution of the global controllability problem is obtained for a class of the triangular systems of O.D.E. that are not feedback linearizable. The introduced class is a generalization of the classes of triangular systems investigated…
A hyperbolic integro-differential equation is considered, as a model problem, where the convolution kernel is assumed to be either smooth or no worse than weakly singular. Well-posedness of the problem is studied in the context of semigroup…
Volterra analysis and its variants have long been prominent among methods for modeling multi-input non-linear systems. The product of Volterra analysis, the Volterra kernels, are particularly suited to quantifying intra- and inter-input…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
In the paper stochastic Volterra equations with noise terms driven by series of independent scalar Wiener processes are considered. In our study we use the resolvent approach to the equations under consideration. We give sufficient…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an…
We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved…