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Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
In this paper we show that, if $T$ is an area-minimizing $2$-dimensional integral current with $\partial T = Q [\![ \Gamma ]\!]$, where $\Gamma$ is a $C^{1,\alpha}$ curve for $\alpha>0$ and $Q$ an arbitrary integer, then $T$ has a unique…
In this paper we consider the solution of monotone inverse problems using the particular example of a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total…
The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
We consider commutator-free exponential integrators as put forward in [Alverman, A., Fehske, H.: High-order commutator-free exponential time-propagation of driven quantum systems. J. Comput. Phys. 230, 5930-5956 (2011)]. For parabolic…
In this paper, we study the existence of at least one positive solution for a nonlinear third-order two-point boundary value problem with integral condition. By employing the Krasnoselskii's fixed point theorem on cones, the existence…
For the general class of pseudo-Finsler spaces with $(\alpha,\beta)$-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has Lorentzian…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a…
Long-term causal inference is an important but challenging problem across various scientific domains. To solve the latent confounding problem in long-term observational studies, existing methods leverage short-term experimental data.…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…
In this preprint we consider fully nonlinear equations in thin domains with oblique boundary condition, finding some new phenomena, in particular the limit equation contains "new terms" of the second, first and zeroth order which don't have…
The convergence of Levenberg-Marquard method is discussed for the inverse problem to reconstruct the storage modulus and loss modulus for the so called scalar model by single interior measurement. The scalar model is the most simplest model…
In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
This paper makes 3 contributions. First, it generalizes the Lindeberg\textendash Feller and Lyapunov Central Limit Theorems to Hilbert Spaces by way of $L^2$. Second, it generalizes these results to spaces in which sample failure and…
A sufficient condition for entanglement in two-mode continuous systems is constructed based on interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number…
This paper deals with the problem of identification of a Robin coefficient (also known as impedance coefficient) in a parabolic PDE from terminal observations of the temperature distributions. The problem is ill-posed in the sense that…