Results 71 to 80 of about 2,057 (240)

Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is λ(1+u2)(p−2)/2u−div((1+|∇u|2)(p−2)/2∇u)−div(c(x)(1+|u|2)(τ+1)/2)+b(x)(1+|∇u|2)(σ+1)/2=finΩ(1+|∇u|2)(p−2)/2∇u+c(x)(1+|u|2)(τ+1)/2)·n̲=0on∂Ω,$$\begin{equation*} {\begin{cases} {}\lambda {(1+ u^2)}^{(p-2)/2}u-{\operatorname{div}}({(1+|\
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo, Maria Rosaria Posteraro   +3 more
wiley   +1 more source

Sparse Reconstructions for Inverse PDE Problems

, 2009
We are concerned with the numerical solution of linear parameter identification problems for parabolic PDE, written as an operator equation $Ku=f$. The target object $u$ is assumed to have a sparse expansion with respect to a wavelet system $Psi={psi_lambda}$ in space-time, being equivalent to a priori information on the regularity of $u=mathbf u ...
openaire   +4 more sources

Continuous analogue to iterative optimization for PDE-constrained inverse problems [PDF]

Inverse Problems in Science and Engineering, 2018
The parameters of many physical processes are unknown and have to be inferred from experimental data. The corresponding parameter estimation problem is often solved using iterative methods such as steepest descent methods combined with trust regions. For a few problem classes also continuous analogues of iterative methods are available.
Boiger, R., Fiedler, A., Hasenauer, J., Kaltenbacher, B.   +3 more
openaire   +3 more sources

Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar, Khaled A. Gepreel, Reham M. A. Shohib, Yakup Yildirim   +3 more
wiley   +1 more source

Application of the inverse Laplace transform techniques to solve the generalized Bagley–Torvik equation including Caputo’s fractional derivative

Partial Differential Equations in Applied Mathematics
This article employs the Laplace transform approach to solve the Bagley–Torvik equation including Caputo’s fractional derivative. Laplace transform is a powerful method for enabling solving integer and non-integer order ODEs and PDEs in engineering and ...
Dania Santina, Kamran, Muhammad Asif, Salma Aljawi, Nabil Mlaiki   +4 more
doaj   +1 more source

Nordgren PINNs to VQE: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics‐Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs were employed to solve Nordgren's equation, which governs fracture width evolution, by embedding physical laws into the neural network ...
Dennis Delali Kwesi Wayo, Sonny Irawan, Mohd Zulkifli Bin Mohamad Noor, Mudasar Zafar, Shynar Juziyeva, Camila Martins Saporetti, Leonardo Goliatt, Randy Hazlett   +7 more
wiley   +1 more source

Numerical differentiation of fractional order derivatives based on inverse source problems of hyperbolic equations

Mathematical Modelling and Analysis
In this paper, we mainly study the numerical differentiation problem of computing the fractional order derivatives from noise data of a single variable function.
Zewen Wang, Shufang Qiu, Xiuxing Rui, Wen Zhang   +3 more
doaj   +1 more source

Meshless solutions of PDE inverse problems on irregular geometries

CoRR
Solving inverse and optimization problems over solutions of nonlinear partial differential equations (PDEs) on complex spatial domains is a long-standing challenge. Here we introduce a method that parameterizes the solution using spectral bases on arbitrary spatiotemporal domains, whereby the basis is defined on a hyperrectangle containing the true ...
James V. Roggeveen, Michael P. Brenner
openaire   +2 more sources

Approximate Reachability for Feedback Linearizable Systems

Optimal Control Applications and Methods, EarlyView.
The backwards reachable set for a dynamical system is the set of states for which there exists a constraint admissible trajectory that reaches a given terminal set. Conventional grid‐based approaches for computing these sets are intractable for many applications.
Vincent Liu, Chris Manzie, Peter M. Dower   +2 more
wiley   +1 more source

A nonsmooth primal-dual method with interwoven PDE constraint solver [PDF]

We introduce an efficient first-order primal-dual method for the solution of nonsmooth PDE-constrained optimization problems. We achieve this efficiency through not solving the PDE or its linearisation on each iteration of the optimization method ...
Valkonen, T, Jensen, Bjørn, Valkonen, Tuomo, Jensen, B   +3 more
core   +2 more sources