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 …
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 …
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 …
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
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 …
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 …
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
share this content in Facebook share this content in Twitter share this content in Linkedin …
share this content in Facebook share this content in Twitter share this content in Linkedin …
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 …
Neumann boundary conditions and boundary observation. The methods we develop here …
Topological optimization via cost penalization
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 …
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 …
involving unknown/variable domains, that penalizes the given boundary condition in the cost …
Periodic Hamiltonian systems in shape optimization problems with Neumann boundary conditions
The recent implicit parametrization theorem, based on simple Hamiltonian systems, allows
the description of domains and their boundaries and, consequently, it provides a general …
the description of domains and their boundaries and, consequently, it provides a general …