Related papers: A Regularization for Time-Fractional Backward Heat…
We consider a boundary value problem in unbounded 2D doubly periodic composite with circular inclusions having arbitrary constant conductivities. By introducing complex potentials, the boundary value problem for the Laplace equation is…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
In a Hilbert setting we aim to study a second order in time differential equation, combining viscous and Hessian-driven damping, containing a time scaling parameter function and a Tikhonov regularization term. The dynamical system is…
In this paper we study the harmonic map heat flow problem for a radially symmetric case. The corresponding partial dfferential equation plays a key role in many analyses of harmonic map heat flow problems. We consider a basic discretization…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…
Current-carrying conductors inevitably experience resistive heating due to the material's finite electrical conductivity. The resulting temperature distribution within the wire has essential implications for structural integrity,…
We develop a flow renormalization approach for periodically-driven quantum systems, which reveals prethermal dynamical regimes and associated timescales via direct correspondence between real time and flow time behavior. In this formalism,…
In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the…
Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order…
This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state…
We consider the initial boundary value problem for the time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and an inhomogeneous initial data $a(x)\in L^{2}(D)$ in a bounded domain $D\subset \mathbb{R}^d$ with…
This paper investigates an inverse source problem for general semilinear stochastic hyperbolic equations. Motivated by the challenges arising from both randomness and nonlinearity, we develop a globally convergent iterative regularization…
Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…
We consider an extension of the well-known Hamilton-Jacobi-Bellman (HJB) equation for fractional order dynamical systems in which a generalized performance index is considered for the related optimal control problem. Owing to the…
In this paper, we study a certain approximation property for a time optimal control problem of the heat equation with $L^\infty$-potential. We prove that the optimal time and the optimal control to the same time optimal control problem for…
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particular, linear approximation frameworks-such as spectral,…
We develop a space-time spectral element method for topology optimization of transient heat conduction. The forward problem is discretized with summation-by-parts (SBP) operators, and interface/boundary and initial/terminal conditions are…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…