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Inverse Problem for Whitham Type Multi-Dimensional Differential Equation with Impulse Effects
AbstractIn the article the questions of unique solvability and determination of the redefinition coefficient function in the inverse problem for...
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Inverse Problems for the Loaded Parabolic-Hyperbolic Equation Involves Riemann–Liouville Operator
AbstractIn this article, the existence and the uniqueness of solution of inverse problems with non-linear gluing condition for the loaded...
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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...
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On One Cauchy Problem for a Hyperbolic Differential-Difference Equation
AbstractWe provide a formulation of the Cauchy problem in a strip for a two-dimensional hyperbolic equation containing a superposition of a...
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The a-Points of the Riemann Zeta-Function and the Functional Equation
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the a-points of the...
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Nonlocal Boundary Value Problem for a Mixed Type Equation with Fractional Partial Derivative
We study the nonlocal boundary value problem for a mixed type equation with the Riemann–Liouville fractional partial derivative. In the hyperbolic...
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A heat equation approach to intertwining
In this paper we present anew approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR...
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Classical Solution to the Cauchy Problem for a Semilinear Hyperbolic Equation in the Case of Two Independent Variables
AbstractIn the upper half-plane, we consider a semilinear hyperbolic partial differential equation of order higher than two. The operator in the...
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Multioutput FOSLS Deep Neural Network for Solving Allen–Cahn Equation
AbstractThis paper utilizes feed-forward neural networks to approximate solutions and their scaled gradients of the Allen–Cahn equation. A...
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Noise Effect on the 2D Stochastic Burgers Equation
By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise, we find the decay properties of the solution to...
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Blow-Up and Global Solvability of the Cauchy Problem for a Pseudohyperbolic Equation Related to the Generalized Boussinesq Equation
Under consideration is the Cauchy problem in the space of continuous functions for a nonlinear strictly hyperbolic equation related to the...
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Determining of a Space Dependent Coefficient of Fractional Diffusion Equation with the Generalized Riemann–Liouville Time Derivative
AbstractThis work investigates an initial-boundary value and an inverse coefficient problem of determining a space dependent coefficient in the...
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Inverse Problems of Determination of the Time-Dependent Coefficient of a Parabolic Equation with Involution and Antiperiodicity Conditions
By the method of separation of variables, we construct the solution of the investigated problem with an unknown coefficient in the differential...
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Numerical Simulation of Inverse Retrospective Problems for a Nonlinear Heat Equation
AbstractA method is proposed for numerically solving the inverse problem of restoring the initial condition for a nonlinear one-dimensional heat...
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On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems
AbstractWe consider the optimal control problem of minimizing the terminal cost functional for a dynamical system whose motion is described by a...
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Homogenization of a Parabolic Equation in a Perforated Domain with a Unilateral Dynamic Boundary Condition: Critical Case
The present paper studies the homogenization of the parabolic equation stated in a domain perforated by “tiny” balls. On the boundary of these...
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Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation
AbstractWe consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of...
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Boundary Integral Operators for the Heat Equation in Time-Dependent Domains
This article provides a functional analytical framework for boundary integral equations of the heat equation in time-dependent domains. More...
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Partial Differential Equation Models
A partial differential equation is an implicit or explicit equation involving derivatives of an unknown functions of more than one independent...