相关论文: Fredholm Property of Nonlocal Problems for Integro…
The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…
We consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on $C^m$-regularity of the free boundary are obtained. In particular, a necessary and…
We develop tools for the analysis of fronts, pulses, and wave trains in spatially extended systems with nonlocal coupling. We first determine Fredholm properties of linear operators, thereby identifying pointwise invertibility of the…
In this work we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic type equation with three lines of type-changing with Caputo fractional derivative in the parabolic part. We equivalently reduce…
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary…
In this note we set up the elliptic and the parabolic Dirichlet problem for linear nonlocal operators. As opposed to the classical case of second order differential operators, here the "boundary data" are prescribed on the complement of a…
We develop a linear theory of very weak solutions for nonlocal eigenvalue problems $\mathcal L u = \lambda u + f$ involving integro-differential operators posed in bounded domains with homogeneous Dirichlet exterior condition, with and…
Unbounded operators corresponding to nonlocal elliptic problems on a bounded region $G\subset\mathbb R^2$ are considered. The domain of these operators consists of functions from the Sobolev space $W_2^m(G)$ being generalized solutions of…
This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at…
We prove the existence of solutions for some integro-differential systems containing equations with and without the drift terms in the H^2 spaces by virtue of the fixed point technique when the elliptic equations contain second order…
The paper is concerned with comparative analysis of differential and integral formulations for boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an antiplane problem for a half-space for an…
Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can be characterized using quantitative, universal energy…
We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic…
This paper concerns autonomous boundary value problems for 1D semilinear hyperbolic PDEs. For time-periodic classical solutions, which satisfy a certain non-resonance condition, we show the following: If the PDEs are continuous with respect…
When extending bifurcation theory of dynamical systems to nonautonomous problems, it is a central observation that hyperbolic equilibria persist as bounded entire solutions under small temporally varying perturbations. In this paper, we…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
We present a boundary integral formulation of the Helmholtz equation with visco-thermal boundary conditions, in two dimensions. Such boundary conditions allow for the accurate simulation of viscous and thermal losses in the vicinity of the…
The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the…
We analyze optimal control problems for multiple Fredholm and Volterra integral equations. These are non Pontryaginian optimal control problems, i.e. an extremum principle of Pontryagin type does not hold. We obtain first order necessary…
This paper considers boundary value problems for a class of singular elliptic operators which appear naturally in the study of asymptotically anti-de Sitter (aAdS) spacetimes. These problems involve a singular Bessel operator acting in the…