Article
Mathematics
Hayat Benchira, M. El Mokhtar Ould El Mokhtar, Atika Matallah
Summary: In this study, the existence of a positive solution for a p-Kirchhoff-type problem with Sobolev exponent is proven.
JOURNAL OF MATHEMATICS
(2022)
Article
Automation & Control Systems
Ciro D'Apice, Umberto De Maio, Peter Kogut
Summary: The study focuses on the optimal control problem for the mixed Dirichlet-Neumann boundary value problem for a strongly nonlinear elliptic equation with exponential nonlinearity in a domain with rough boundary. The surface traction density acting on a part of the rough boundary is considered as the control variable, with the objective being to minimize the discrepancy between a given distribution and the current system state. The research deals with cases of nonlinearity where a solution of the state equation cannot be guaranteed for a given control, and proves the consistency of the original optimal control problem along with showing the existence of a unique optimal solution by defining a suitable functional class. Additionally, a first-order optimality system is derived under the assumption that the optimal solution is slightly more regular.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2021)
Article
Mathematics, Applied
Peter Kogut, Yaroslav Kohut, Rosanna Manzo
Summary: In this paper, we discuss the optimal control problem for the evolutionary Perona-Malik equations with the Neumann boundary condition and introduce a variant of its approximation using a model with fictitious control. We also show the consistency and well-posedness of a special family of regularized optimization problems for linear parabolic equations.
RICERCHE DI MATEMATICA
(2022)
Article
Automation & Control Systems
Viorel Barbu
Summary: This work focuses on the existence of optimal controllers for the Bolza optimal control problem governed by the nonlinear Fokker-Planck equation in L1(Rd) with control input in the drift term. The solution to the control state system is a weak (mild) solution obtained from a vanishing viscosity approximation scheme. In particular, we prove the existence of a stochastic Markov optimal controller in feedback form for the stochastic optimal control problem governed by McKean-Vlasov SDEs.
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Yuxia Guo, Yichen Hu
Summary: This paper investigates the prescribed curvature problem involving the polyharmonic operator on SN, and constructs a new type of solution using the Lyaponov Schmidt reduction arguments and gluing method.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2022)
Article
Mathematics, Applied
Claudianor O. Alves, Vincenzo Ambrosio, Cesar E. Torres Ledesma
Summary: This paper examines the existence of solutions for a class of magnetic semilinear Schrodinger equations under certain conditions.
MILAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Susanne C. Brenner, Jose C. Garay, Li-Yeng Sung
Summary: In this study, multiscale finite element methods are explored for an elliptic distributed optimal control problem with rough coefficients. These methods are based on the (local) orthogonal decomposition methodology proposed by Malqvist and Peterseim.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics
Ru-Yu Lai, Ting Zhou
Summary: In this paper, the forward and the inverse problem for the fractional magnetic Schrodinger equation with a nonlinear electric potential are studied. The maximum principle for the linearized equation is first obtained and applied to show the well-posedness of the problem under suitable assumptions for the exterior condition. Then the uniqueness in recovering both the magnetic and the nonlinear electric potentials, assumed to be analytic in terms of the solution, from the exterior data of the solution is obtained.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
A. Aghajani, C. Cowan, A. Moameni
Summary: In this paper, we consider a Gelfand problem and study the regularity of the extremal solution. We obtain improved compactness due to the annular nature of the domain and further compactness under certain monotonicity assumptions on the domain.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Majid Darehmiraki, Arezou Rezazadeh, Ali Ahmadian, Soheil Salahshour
Summary: This paper proposes a Lagrange polynomial-based method for solving the optimal control problem governed by the elliptic convection-diffusion partial differential equation. The state variable and adjoint variable are discretized using the barycentric interpolation method, and the convergence of the proposed method is proved. Numerical experiments are conducted to illustrate the theoretical findings.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Multidisciplinary Sciences
Anass Ourraoui, Maria Alessandra Ragusa
Summary: This paper investigates the existence of solutions to anisotropic variable exponent problems involving the p ->(.)-Laplacian using the variational method as the main tool. The presented result shows that the Ambrosetti-Rabinowitz-type conditions are not necessary for the existence of solutions.
Article
Mathematics, Applied
Pardeep Kumar, Kush Kinra, Manil T. Mohan
Summary: In this paper, an inverse problem for three dimensional viscoelastic fluid flow equations, specifically for Kelvin-Voigt fluids and Oseen type equations, is considered. Using mathematical techniques, local and global existence and uniqueness results are obtained for these inverse problems.
Article
Mathematics
Matti Lassas, Tony Liimatainen, Leyter Potenciano-Machado, Teemu Tyni
Summary: This article discusses the recovery of a potential associated with a semi-linear wave equation on Rn+1, showing that the unknown potential can be recovered in a H & ouml;lder stable way. The method presented is constructive and based on higher order linearization, and a uniqueness result is also obtained. The article also addresses the forward problem of the equation.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Zhanna D. Totieva
Summary: This study addresses a multidimensional inverse problem for a viscoelasticity equation. The aim is to reconstruct both the displacement and convolutional kernel simultaneously based on overdetermination conditions. The main result is a theorem that proves the global unique solvability of the inverse problem in a class of functions that are continuous in the time variable and analytic in the space variable. The study utilizes the methods of scales of Banach spaces and weight norms in the class of continuous functions.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
A. Aghajani, C. Cowan
Summary: The problem investigates a supercritical problem near the origin on an open unit ball B-1 centered at the origin in R-N, where a positive weak solution u exists satisfying specific boundary conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)