All Research Papers Published In Applied Mathematics & Optimization

Research Article
4
10.1007/s00245-023-10094-2

Global Solution and Optimal Control of an Epidemic Propagation with a Heterogeneous Diffusion

Jan 09, 2024
Applied Mathematics & Optimization
Pierluigi Colli + 2 more +2

Research Article
1
10.1007/s00245-023-10098-y

Effects of Kelvin–Voigt Damping on the Stability of (Thermo)Elastic Timoshenko System with Second Sound

Dec 29, 2023
Applied Mathematics & Optimization
Jianan Cui + 1 more +1

Research Article
2
10.1007/s00245-023-10082-6

Continuity Properties of Pullback and Pullback Exponential Attractors for Non-autonomous Plate with $$p-$$Laplacian

Nov 30, 2023
Applied Mathematics & Optimization
Moncef Aouadi

Research Article
14
10.1007/s00245-023-10044-y

Learning-Informed Parameter Identification in Nonlinear Time-Dependent PDEs

Aug 23, 2023
Applied Mathematics & Optimization
Christian Aarset + 2 more +2

We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns: physical parameter, state and nonlinearity. Inspired by advances in machine learning, we approximate the nonlinearity via a neural network, whose parameters are learned from measurement data. The latter is assumed to be given as noisy observations of the unknown state, and both the state and the physical parameters are identified simultaneously with the parameters of the neural network. Moreover, diverging from the classical approach, the proposed all-at-once setting avoids constructing the parameter-to-state map by explicitly handling the state as additional variable. The practical feasibility of the proposed method is confirmed with experiments using two different algorithmic settings: A function-space algorithm based on analytic adjoints as well as a purely discretized setting using standard machine learning algorithms.

Research Article
6
10.1007/s00245-023-10043-z

Long-Time Dynamics of the Wave Equation with Nonlocal Weak Damping and Super-Cubic Nonlinearity in 3-D Domains, Part II: Nonautonomous Case

Aug 17, 2023
Applied Mathematics & Optimization
Senlin Yan + 3 more +3

Research Article
2
10.1007/s00245-023-10040-2

Estimates of Exponential Convergence for Solutions of Stochastic Nonlinear Systems

Aug 11, 2023
Applied Mathematics & Optimization
Tomás Caraballo + 2 more +2

Research Article
5
10.1007/s00245-023-10033-1

Reverse Isoperimetric Inequality for the Lowest Robin Eigenvalue of a Triangle

Aug 11, 2023
Applied Mathematics & Optimization
David Krejčiřík + 2 more +2

We consider the Laplace operator on a triangle, subject to attractive Robin boundary conditions. We prove that the equilateral triangle is a local maximiser of the lowest eigenvalue among all triangles of a given area provided that the negative boundary parameter is sufficiently small in absolute value, with the smallness depending on the area only. Moreover, using various trial functions, we obtain sufficient conditions for the global optimality of the equilateral triangle under fixed area constraint in the regimes of small and large couplings. We also discuss the constraint of fixed perimeter.

Research Article
21
10.1007/s00245-023-09997-x

Accelerated Gradient Methods Combining Tikhonov Regularization with Geometric Damping Driven by the Hessian

May 31, 2023
Applied Mathematics & Optimization
Hedy Attouch + 3 more +3

Research Article
10.1007/s00245-023-10012-6

System of Nonlinear Second-Order Parabolic Partial Differential Equations with Interconnected Obstacles and Oblique Derivative Boundary Conditions on Non-Smooth Time-Dependent Domains

May 31, 2023
Applied Mathematics & Optimization
Manal Jakani

Research Article
4
10.1007/s00245-023-10008-2

A Strong Averaging Principle Rate for Two-Time-Scale Coupled Forward–Backward Stochastic Differential Equations Driven by Fractional Brownian Motion

May 31, 2023
Applied Mathematics & Optimization
Jie Xu + 2 more +2