相关论文: On a class of inverse problems for a heat equation…

Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a…

Results on well-posedness of three inverse problems with integral conditions on a bounded interval for the generalized Korteweg-de Vries equation without any restrictions on the growth rate of nonlinearity are established. Either the…

We consider the Schrodinger operator in n-dimensional rectangular domains with either Dirichlet or Neumann boundary conditions on the faces and study the constraints on the potential imposed by fixing the spectrum of the operator.We study…

From the final and interior temperature measurements identifying the source term with initial temperature simultaneously is an inverse heat conduction problem which is a kind of ill-posed. The optimal control framework has been found to be…

In this paper we consider the problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in one-dimensional heat equation in the case of nonlocal boundary and integral overdetermination…

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented…

The paper considers the integral Volterra equations of the first kind which are related to the inverse boundary-value heat conduction problem. The algorithms have been developed to numerically solve the respective integral equations, which…

We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diffeomorphism $\phi$. We analyze the maps that assign to the…

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied.…

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…

We consider inverse boundary value problems for elliptic equations of second order of determining coefficients by Dirichlet-to-Neumann map on subboundaries, that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus…

We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets. As an inverse data we use an analog of a response operator…

We present a class of non-cylindrical domains where Dirichlet-type problems for parabolic equations, such as the heat equation, can be posed and solved. The regularity for the boundary of this class of domains is a mixed Lipschitz…

This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet…

In the present article we present a particular combination of boundary problems for the inhomogeneous tri-analytic equation: the Neumann-(Dirichlet-Neuman) problem and the (Dirichlet-Neumann)-Dirichlet problem. In order to obtain the…

We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…

The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

In this paper we explore the weak solutions of the Cauchy problem and an inverse source problem for the heat equation in the quantum calculus, formulated in abstract Hilbert spaces. For this we use the Fourier series expansions. Moreover,…