Related papers: Simultaneous recoveries for semilinear parabolic s…
We consider the inverse problem of determining a general semilinear term appearing in nonlinear parabolic equations. For this purpose, we derive a new criterion that allows to prove global recovery of some general class of semilinear terms…
In this short note, we investigate simultaneous recovery inverse problems for semilinear elliptic equations with partial data. The main technique is based on higher order linearization and monotonicity approaches. With these methods at…
We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
In this paper, we consider the inverse boundary problems of recovering the time-dependent nonlinearity and damping term for a semilinear wave equation on a Riemannian manifold. The Carleman estimate and the construction of Gaussian beams…
This article is devoted to forward and inverse problems associated with time-independent semilinear nonlocal wave equations. We first establish comprehensive well-posedness results for some semilinear nonlocal wave equations. The main…
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of…
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…
In this paper, we consider an inverse problem to determine a semilinear term of a parabolic equation from a single boundary measurement of Neumann type. For this problem, a reconstruction algorithm is established by the spectral…
In this work, we consider the inverse problem of simultaneously recovering two classes of quasilinear terms appearing in a parabolic equation from boundary measurements. It is motivated by several industrial and scientific applications,…
This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open…
We consider the problem of recovering a nonlinear potential function in a nonlinear Schr\"odinger equation on transversally anisotropic manifolds from the linearized Dirichlet-to-Neumann map at a large wavenumber. By calibrating the complex…
We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…
In this paper we are concerned with the initial boundary value problems of linear and semi-linear parabolic equations with mixed boundary conditions on non-cylindrical domains in spatial-temporal space. We obtain the existence of a weak…
We study the stability issue for the inverse problem of determining a coefficient appearing in a Schr\"odinger equation defined on an infinite cylindrical waveguide. More precisely, we prove the stable recovery of some general class of…
In this paper, we study the inverse problem for determining an unknown time-dependent source coefficient in a semilinear pseudo-parabolic equation with variable coefficients and Neumann boundary condition. This unknown source term is…
We propose a global convergent numerical method to reconstruct the initial condition of a nonlinear parabolic equation from the measurement of both Dirichlet and Neumann data on the boundary of a bounded domain. The first step in our method…