Search
Search Results
-
Nonlocal Transformations with Additional Variables. Forced Symmetries
The concept of nonlocal transformation with additional variables is proposed, developed, and applied to the determination of additional symmetries of...
-
Nonlocal Integrable Equations in Soliton Theory
This article is to provide a brief overview of the study of nonlocal integrable equations in soliton theory. The concept of nonlocality is explained,...
-
Nonlocal Symmetries of the System of Chemotaxis Equations with Derivative Nonlinearity
By using nonlocal equivalence transformations, the system of chemotaxis equations is associated with a system of convection-diffusion equations. The...
-
Shape optimization for interface identification in nonlocal models
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider...
-
Quasi-Periodic Solutions to the Nonlocal Nonlinear Schrödinger Equations
A hierarchy of nonlocal nonlinear Schrödinger equations is derived by using the Lenard gradients and the zero-curvature equation. According to the...
-
Optimal Control of Nonlocal Continuity Equations: Numerical Solution
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general...
-
A Nonlocal Initial Conditional Boundary Value Problem on Metric Graph
The main task of the present research is a nonlocal boundary value problem for a time-fractional differential equation involving the Hilfer...
-
Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem: without Solitons
In this work, we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the...
-
Pattern Bifurcation in a Nonlocal Erosion Equation
AbstractThis paper considers a periodic boundary value problem for a nonlinear partial differential equation with a deviating spatial variable. It is...
-
Nonlocal minimal surfaces: recent developments, applications, and future directions
Recently, we have found that nonlocal minimal surfaces enjoy notably stronger regularity estimates than classical minimal surfaces. This survey paper...
-
Positive solutions, positive radial solutions and uniqueness results for some nonlocal elliptic problems
In this paper, we prove existence of a positive solution to a one-dimensional nonlocal elliptic problem and existence of a positive radial solution...
-
Diffusion in Media with Membranes and Some Nonlocal Parabolic Problems
We establish the classical solvability of a certain conjugation problem for one-dimensional (with respect to a spatial variable) Kolmogorov backward...
-
Nonlocal (In Time) Problem for the Evolutionary Equation with Fractional Differential Operator
We establish the correct solvability of a multipoint nonlocal (in time) problem for the evolutionary equation with operator of fractional...
-
Transmutation Operators Based on Homotope Analysis for Nonlocal Boundary Value Problems
AbstractTransmutation operators nonlocal boundary value problems in terms of the homotopic analysis method is used to solve and research nonlocal...
-
Nonlinear Inverse Problems for Parabolic Equations with Time–Dependent Coefficients. Reduction to Nonlocal Problems with Samarskii–Ionkin Type Conditions
We consider coefficient inverse problems of finding a solution and a time-dependent coefficient of a parabolic equation under boundary...
-
Bäcklund Transformations of the Relativistic Schrödinger Equation
AbstractWe study the system of equations obtained on the basis of the relativistic Schrödinger equation and relating the potential, amplitude, and...
-
The Commutative Property of Reciprocal Transformations and Dimensional Deformations
The paper aims to analyze the commutative property of reciprocal transformations and dimensional deformations using conservation laws. First, a...
-
Time-Nonlocal Problem for Evolutionary Equations with Pseudodifferential Operators in Spaces of Type S
We consider evolutionary equations with fractional differentiation operators whose restrictions to certain spaces of type S coincide with...
-
A discretization method for nonlocal diffusion type equations
In this paper we consider a numerical scheme for the treatment of an integro-differential equation. The latter represents the formulation of a...
-
Solvability and Volterra property of nonlocal problems for mixed fractional-order diffusion-wave equation
The paper is devoted to the study of one class of problems with nonlocal conditions for a mixed diffusion-wave equation with two independent...