相关论文: The Initial Value Problem For Maximally Non-Local …

Non-locality is being intensively studied in various PDE-contexts and in variational problems. The numerical approximation also looks challenging, as well as the application of these models to Continuum Mechanics and Image Analysis, among…

We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…

In this paper we consider an initial boundary value problem for a semilinear parabolic equation with nonlinear nonlocal boundary condition. We prove comparison principle, the existence theorem of a local solution and study the problem of…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special…

We study the Cauchy problem for non-linear non-local operators that may be degenerate. Our general framework includes cases where the jump intensity is allowed to depend on the values of the solution itself, e.g. the porous medium equation…

We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…

For many cellular automata, it is possible to express the state of a given cell after $n$ iterations as an explicit function of the initial configuration. We say that for such rules the solution of the initial value problem can be obtained.…

This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…

We consider the abstract initial value problem for the system of evolution equations which describe motion of micropolar fluids with heat conduction in a bounded domain. This problem has uniquely a mild solution locally in time for general…

We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…

The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…

We propose dynamical systems defined on algebra of lattices, which we call `lattice equations'. We give exact general solutions of initial value problems for a class of lattice equations, and evaluate the complexity of the solutions.…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

Several definitions for the average local value and local variance of a quantum observable are examined and compared with their classical counterparts. An explicit way to construct an infinite number of these quantities is provided. It is…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

In this work, we study the initial value problem associated with an abstract integrodifferential equation in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and a blow-up alternative for regular mild…

In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…