Related papers: The dimensional reduction method for solving a non…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of…
In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…
This paper considers one-dimensional heat transfer in a media with temperature-dependent thermal conductivity. To model the transient behavior of the system, we solve numerically the one-dimensional unsteady heat conduction equation with…
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…
Time-periodic weak solutions for a coupled hyperbolic-parabolic system are obtained. A linear heat and wave equation are considered on two respective $d$-dimensional spatial domains that share a common $(d-1)$-dimensional interface…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
The enclosure method was originally introduced for inverse problems of concerning non-destructive evaluation governed by elliptic equations. It was developed as one of useful approaches in inverse problems and applied for various equations.…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
The Runge--Kutta (RK) discontinuous Galerkin (DG) method is a mainstream numerical algorithm for solving hyperbolic equations. In this paper, we use the linear advection equation in one and two dimensions as a model problem to prove the…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional…
We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
The aim of this paper is to establish the framework of the enclosure method for some class of inverse problems whose governing equations are given by parabolic equations with discontinuous coefficients. The framework is given by considering…
An inverse problem of finding an unknown heat source for a class of linear parabolic equations is considered. Such problems can typically be converted to a direct problem with non-local conditions in time instead of an initial value…
Direct shooting is an efficient method to solve numerical optimal control. It utilizes the Runge-Kutta scheme to discretize a continuous-time optimal control problem making the problem solvable by nonlinear programming solvers. However,…
We propose an efficient way of solving optimal control problems for rigid-body systems on the basis of inverse dynamics and the multiple-shooting method. We treat all variables, including the state, acceleration, and control input torques,…