Results 21 to 30 of about 14,895 (148)

Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

Boundary Value Problems, 2020
In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerkin method.
Salah Boulaaras, Nadjat Doudi
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Solve High-Dimensional Reflected Partial Differential Equations by Neural Network Method

Mathematical and Computational Applications, 2023
Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs.
Xiaowen Shi, Xiangyu Zhang, Renwu Tang, Juan Yang   +3 more
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ANN-based methods for solving partial differential equations: a survey

Arab Journal of Basic and Applied Sciences, 2022
Traditionally, partial differential equation (PDE) problems are solved numerically through a discretization process. Iterative methods are then used to determine the algebraic system generated by this process. Recently, scientists have emerged artificial
Danang, A. Pratama, Maharani A. Bakar, N. B. Ismail, Mashuri M   +3 more
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Collaborating PDE solvers

Applied Numerical Mathematics, 1992
The authors describe a new methodology for solving systems of partial differential equations. They explain the methodology in the case of two- dimensional second-order linear elliptic problems of the form \(L_ i{\mathbf u}_ i = f_ i \text{ for }(x, y) \in D_ i\), \(M_ i{\mathbf u}_ i = g_ i \text{ for }(x, y) \in \partial D_ i\), \(i=1,2,...,m\), where
McFaddin, H. S., Rice, John R.
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Patient-Derived Explants as a Precision Medicine Patient-Proximal Testing Platform Informing Cancer Management

Frontiers in Oncology, 2021
Precision medicine approaches that inform clinical management of individuals with cancer are progressively advancing. Patient-derived explants (PDEs) provide a patient-proximal ex vivo platform that can be used to assess sensitivity to standard of care ...
Abby R. Templeton, Abby R. Templeton, Abby R. Templeton, Abby R. Templeton, Penny L. Jeffery, Penny L. Jeffery, Penny L. Jeffery, Penny L. Jeffery, Patrick B. Thomas, Patrick B. Thomas, Patrick B. Thomas, Patrick B. Thomas, Mahasha P. J. Perera, Mahasha P. J. Perera, Mahasha P. J. Perera, Mahasha P. J. Perera, Mahasha P. J. Perera, Gary Ng, Gary Ng, Alivia R. Calabrese, Alivia R. Calabrese, Alivia R. Calabrese, Alivia R. Calabrese, Clarissa Nicholls, Clarissa Nicholls, Clarissa Nicholls, Nathan J. Mackenzie, Nathan J. Mackenzie, Nathan J. Mackenzie, Nathan J. Mackenzie, Jack Wood, Jack Wood, Jack Wood, Laura J. Bray, Laura J. Bray, Laura J. Bray, Ian Vela, Ian Vela, Ian Vela, Ian Vela, Ian Vela, Erik W. Thompson, Erik W. Thompson, Elizabeth D. Williams, Elizabeth D. Williams, Elizabeth D. Williams, Elizabeth D. Williams   +46 more
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Asymptotic analysis of the biharmonic Schrödinger equation with fractional damping

Boundary Value Problems
In this paper, we study the decay behavior of solutions to the biharmonic Schrödinger equation under the effect of internal fractional damping. By employing semigroup theory and energy methods, we establish well-posedness results and investigate the long-
Khadidja Fekirini, Naima Louhibi, Ibrahim Meradjah, Salah Boulaaras, Mohamed Hocine Braiki   +4 more
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PDE-PRESERVING PROPERTIES [PDF]

Journal of the Korean Mathematical Society, 2005
A continuous linear operator \(T\) on the space of entire functions in \(d\) variables is called PDE-preserving for a given set \(\mathbb{P}\subseteq\mathbb{C}[\xi_1,\ldots,\xi_d]\) of polynomials if \(T\ker P(D)\subseteq P(D)\) for all \(P\in\mathbb P\), where \(P(D)\) is the differential operator obtained by replacing each variable \(\xi_j\) by ...
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Performance of GRKM-method for solving classes of ordinary and partial differential equations of sixth-orders

Open Engineering
A general quasilinear sixth-order ordinary differential equation (ODE) is an important class of ODEs. The primary objective of this study is to establish a numerical method for solving a general class of quasilinear sixth-order partial differential ...
Mechee Mohammed S., Kadhim Murtadha A., Yazdani Cherati AllahBakhsh   +2 more
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Theoretical and numerical studies of the blow-up of a degenerate nonlinear reaction–diffusion problem with source terms

Applied Mathematics in Science and Engineering
In this paper, we focus on the phenomenon of blow-up of solutions for semilinear and degenerate (time-derivative) parabolic equation systems with additional source terms.
Bariza Sidhoum, Nadjat Doudi, Lamine Nisse, Asma Alharbi, Salah Boulaaras   +4 more
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PDE and Extrafunctions

Rocky Mountain Journal of Mathematics, 2004
Based on the first author's construction of hyperreal numbers and hyperfunctionals [Lect. Notes Pure Appl. Math. 238, 81--117, Dekker, New York (2004; Zbl 1094.46508)]. The present paper investigates solvability of linear first order Cauchy problems in a similar setting of generalized functions, the space of extrafunctions.
Burgin, Mark, Ralston, James
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