Related papers: The Airy equation with nonlocal conditions

We introduce a new approach to constructing analytic solutions of the linear PDEs describing elastodynamics. This approach is illustrated for the case of a homogeneous isotropic half-plane body satisfying arbitrary initial conditions and…

We present and discuss the derivation of a nonlinear non-local integro-differential equation for the macroscopic time evolution of the conserved order parameter of a binary alloy undergoing phase segregation. Our model is a d-dimensional…

In this paper, we study a time-fractional subdiffusion equation with a nonlinear nonlocal initial condition involving the unknown solution at the final time. The considered problem is formulated using the Caputo fractional derivative of…

In this paper we analyze a nonlinear abstract evolution equation with an infinite number of time-dependent time delays and a Lipschitz continuous nonlinear term. By using a fixed point argument we prove the existence of a mild solution.…

The aim of this paper is to provide the first application of Theorem 3 of [2] in a case where the dependence of the underlying equation from the real parameter is not of affine type.

This note deals with the boundary control problem of a nonhomogeneous flexible wing evolving under unsteady aerodynamic loads. The wing is actuated at its tip by flaps and is modeled by a distributed parameter system consisting of two…

A subdiffusion problem in which the diffusion term is related to a stable stochastic process is introduced. Linear models of these systems have been studied in a general way, but non-linear models require a more specific analysis. The model…

This paper presents some sufficient conditions for the existence of solutions of fractional differential equation with nonlocal multi-point boundary conditions involving Caputo fractional derivative and integral boundary conditions. Our…

There has been considerable recent interest in solving non-local equations of motion which contain an infinite number of derivatives. Here, focusing on inflation, we review how the problem can be reformulated as the question of finding…

In this paper, we consider initial-boundary value problems for two-component nonlinear systems of time-fractional diffusion equations with the homogeneous Neumann boundary condition and non-negative initial values. The main results are the…

In this note, we announce a systematic analysis of continuous dependence on the data in classical spaces for the initial-boundary-value problem of the diffusion equation on the half-line, with data that are not necessarily compatible at the…

We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…

In this work, we are concerned with a nonlinear wave equation with variable exponents. A distributive delay is imposed into the damping term with variable exponents nonlinearity. Firstly, we show that the global nonexistence time can be…

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…

The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…

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…

We consider a class of nonlinear Schroedinger equation in three space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…

In the Cauchy problem of general relativity one considers initial data that satisfies certain constraints. The evolution equations guarantee that the evolved variables will satisfy the constraints at later instants of time. This is only…

We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…