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Discussion Paper: A New Mathematical Framework for Representation and Analysis of Coupled PDEs
IFAC-PapersOnLine, 2019 We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions.
Peet, Matthew +3 more
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Mathematical modelling of chemical engineering systems by finite element analysis using PDE/PROTRAN
Computers & Mathematics with Applications, 1988 The PDE/PROTRAN program package is presented (PROTRAN being a powerful preprocessor), theoretical algorithm aspects as well as practical references on two interesting engineering problems. This package can be used to solve two-dimensional problems governed by partial differential equations, like steady-state or time-dependent, as well as eigenvalue ...
Mills, P.L., Ramachandran, P.A.
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Mathematical Analysis of the PDE Model for the Consensus-based Optimization
In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a diffusion term that is both singular and degenerate. By employing a regularization procedure in combination with a
Wang, Jinhuan, Li, Keyu, Huang, Hui
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, 2020 The variability of the data and the incomplete knowledge of the true physics require the incorporation of randomness into the formulation of mathematical models. In this setting, the deterministic numerical methods cannot capture the propagation of the uncertainty from the inputs to the model output.
Calatayud, Julia +2 more
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Open PhysicsAbstract To comprehend nonlinear dynamics, one must have access to soliton solutions, which faithfully portray the actions of numerous physical systems and nonlinear equations. Notable nonlinear equations in relativistic physics, quantum field theory, nonlinear optics, dispersive wave phenomena, contemporary ...
Hossain Md Dulal +5 more
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Mathematical Biosciences and Engineering<abstract><p>This paper is concerned with the PDE (partial differential equation) and numerical analysis of a modified one-dimensional intravascular stent model. It is proved that the modified model has a unique weak solution by using the Galerkin method combined with a compactness argument. A semi-discrete finite-element method and a fully
Xiaobing Feng, Tingao Jiang
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Mathematical modeling and analysis of PDE-models for semiconductor devices
, 2017 Zusammenfassungen in Deutsch und ...
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Alexandria Engineering JournalUnfortunately, the scientific research concerned with the micro-scale mathematical models in plasma has very few numbers compared with the other mathematical models. However, the microscopic fields are related to all modern technology like nano and micro technology, quantum computers, and many other essential applications.
Taha Zakaraia Abdel Wahid +2 more
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, 2014 A particular feature of certain microelectromechanical systems (MEMS) is the appearance of a so-called "pull-in" instability, corresponding to a singularity in the underlying PDE model. We here consider a transient MEMS model and its optimal control via the dielectric properties of the membrane and/or the applied voltage. In contrast to the static case,
Clason, Christian, Kaltenbacher, Barbara
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