Mathematics of nonlinear acoustics

B Kaltenbacher - Evolution Equations and Control Theory, 2015 - aimsciences.org
The aim of this paper is to highlight some recent developments and outcomes in the
mathematical analysis of partial differential equations describing nonlinear sound …

Necessary conditions for the optimal control of a shape optimization problem with non-smooth PDE constraints

L Betz - arxiv preprint arxiv:2409.15039, 2024 - arxiv.org
This paper is concerned with the derivation of necessary conditions for the optimal shape of
a design problem governed by a non-smooth PDE. The main particularity thereof is the lack …

Optimal control of a non-smooth elliptic PDE with non-linear term acting on the control

L Betz - arxiv preprint arxiv:2407.06726, 2024 - arxiv.org
This paper continues the investigations from [7] and is concerned with the derivation of first-
order conditions for a control constrained optimization problem governed by a non-smooth …

A level set approach for damage identification of continuum structures based on dynamic responses

W Zhang, Z Du, G Sun, X Guo - Journal of Sound and Vibration, 2017 - Elsevier
The present paper aims to propose a novel approach for damage identification of continuum
structures based on their dynamic performances. The main idea is resorting to the level set …

[HTML][HTML] Iterated Hamiltonian type systems and applications

D Tiba - Journal of Differential Equations, 2018 - Elsevier
We discuss, in arbitrary dimension, certain Hamiltonian type systems and prove existence,
uniqueness and regularity properties, under the independence condition. We also …

Implicit functions and parametrizations in dimension three: generalized solutions

MR Nicolai, D Tiba - Discrete and Continuous Dynamical Systems, 2014 - aimsciences.org
Implicit functions and parametrizations in dimension three: Generalized solutions AIMS
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Optimality conditions and Lagrange multipliers for shape and topology optimization problems

D Tiba - arxiv preprint arxiv:2210.02688, 2022 - arxiv.org
We discuss first order optimality conditions for geometric optimization problems with
Neumann boundary conditions and boundary observation. The methods we develop here …

Topological optimization via cost penalization

CM Murea, D Tiba - 2019 - projecteuclid.org
We consider general shape optimization problems governed by Dirichlet boundary value
problems. The proposed approach may be extended to other boundary conditions as well. It …

A penalization approach in shape optimization

D Tiba - Atti della Accademia Peloritana dei Pericolanti-Classe …, 2018 - cab.unime.it
We introduce a new approximation technique in general shape optimization problems,
involving unknown/variable domains, that penalizes the given boundary condition in the cost …

Periodic Hamiltonian systems in shape optimization problems with Neumann boundary conditions

CM Murea, D Tiba - Journal of Differential Equations, 2022 - Elsevier
The recent implicit parametrization theorem, based on simple Hamiltonian systems, allows
the description of domains and their boundaries and, consequently, it provides a general …