相关论文: Spectral Optimization Problems
We investigate a shape optimization problem of the Polya-Szego type and prove some results on symmetry and asymmetry of extremal domains.
In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the…
In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…
The model problem of a plane angle for a second-order elliptic system subject to Dirichlet, mixed, and Neumann boundary conditions is analyzed. For each boundary condition, the existence of solutions of the form $r^\lambda v$ is reduced to…
Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.
An accurate approximation of solutions to elliptic problems in infinite domains is challenging from a computational point of view. This is due to the need to replace the infinite domain with a sufficiently large and bounded computational…
In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of boundary value problems. M-functions are defined for general…
This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…
The main tool to study a second order optimality problem is the Hessian operator associated to the cost function that defines the optimization problem. By regarding an orthogonal Stiefel manifold as a constraint manifold embedded in an…
Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving the eigenvalue problem $Lu=\lambda u$ for an elliptic partial differential…
The main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential…
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…
In this paper we prove the existence of an optimal domain $\Omega_{opt}$ for the shape optimization problem $$\max\Big\{\lambda_q(\Omega)\ :\ \Omega\subset D,\ \lambda_p(\Omega)=1\Big\},$$ where $q<p$ and $D$ is a prescribed bounded subset…
This work concerns with the existence of solutions for the following class of nonlocal elliptic problems \begin{equation*}\label{00} \left\{ \begin{array}{l} (-\Delta)^{s}u + u = |u|^{p-2}u\;\;\mbox{in $\Omega$},\\ u \geq 0 \quad \mbox{in}…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…
This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…