Related papers: Fredholm Property of Nonlocal Problems for Integro…
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
In this paper, we investigate the well-posedness theory for the MHD boundary layer system in two-dimensional space. The boundary layer equations are governed by the Prandtl type equations that are derived from the full incompressible MHD…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
Our main contributions include proving sufficient conditions for the existence of solution to a second order problem with nonzero nonlocal initial conditions, and providing a comprehensive analysis using fundamental solutions and…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…
Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations…
Nonlocal problems for higher-order elliptic operators in dihedral and plane angles are considered. The Green formula is obtained, which leads to adjoint problems that take the form of nonlocal transmission problems in dihedral and plane…
In this paper we study the existence of solutions to the following generalized nonlinear two-parameter problem \begin{equation*} a(u, v) \; =\; \lambda\, b(u, m) + \mu\, m(u, v) + \varepsilon\, F(u, v), \end{equation*} for a triple $(a, b,…
In this article we are concerned with an inverse initial boundary value problem for a non-linear wave equation in space dimension $n\geq 2$. In particular we consider the so called interior determination problem. This non-linear wave…
We consider elliptic problems with nonclassical boundary conditions that contain additional unknown functions on the border of the domain of the elliptic equation and also contain boundary operators of higher orders with respect to the…
We investigate Lawruk elliptic boundary-value problems for homogeneous differential equations in a two-sided refined Sobolev scale. These problems contain additional unknown functions in the boundary conditions of arbitrary orders. The…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
This paper deals with a parabolic partial differential equation that includes a non-linear nonlocal in time term. This term is the product of a so-called interaction potential and the solution of the problem. The interaction potential…
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local. We show the…
In this paper, we consider a class of variational problems with integral functionals involving nonlocal gradients. These models have been recently proposed as refinements of classical hyperelasticity, aiming for an effective framework to…
A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…
We consider a periodic-parabolic eigenvalue problem with a non-negative potential $\lambda m$ vanishing on a non-cylindrical domain $D_m$ satisfying conditions similar to those for the parabolic maximum principle. We show that the limit as…