Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps [PDF]
, 2013 Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities ...
Dolean Maini, Victorita +5 more
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Weak TransNet: A Petrov-Galerkin Based Neural Network Method for Solving Elliptic PDEs [PDF]
Journal of Scientific ComputingWhile deep learning has achieved remarkable success in solving partial differential equations (PDEs), it still faces significant challenges, particularly when the PDE solutions have low regularity or singularities. To address these issues, we propose the
Zhihang Xu, Min Wang, Zhu Wang
semanticscholar +1 more source
Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions [PDF]
Annales de l'Institut Henri Poincare. Analyse non linéar, 2019 We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to a coupled system of non-linear PDEs where the moving part of the boundary is an unknown of the ...
B. Muha, S. Schwarzacher
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On a Modified Form of Navier-Stokes Equations for Three-Dimensional Flows
The Scientific World Journal, 2015 A rephrased form of Navier-Stokes equations is performed for incompressible, three-dimensional, unsteady flows according to Eulerian formalism for the fluid motion. In particular, we propose a geometrical method for the elimination of the nonlinear terms
J. Venetis
doaj +1 more source
A moment approach for entropy solutions to nonlinear hyperbolic PDEs [PDF]
Mathematical Control and Related Fields, 2018 We propose to solve polynomial hyperbolic partial differential equations (PDEs) with convex optimization. This approach is based on a very weak notion of solution of the nonlinear equation, namely the measure-valued (mv) solution, satisfying a linear ...
S. Marx +3 more
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Global weak solutions and asymptotics of a singular PDE-ODE Chemotaxis system with discontinuous data [PDF]
Science China Mathematics, 2020 This paper is concerned with the well-posedness and large-time behavior of a two dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-Hopf type transformation into a parabolic-hyperbolic system and show that the solution of the transformed system converges to a constant ...
Peng, Hongyun +2 more
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Blow-up behavior of collocation solutions to Hammerstein-type volterra integral equations [PDF]
, 2013 We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time.
Brunner, Hermann, Yang, Z.W.
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Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost
Abstract and Applied Analysis, 2014 Transforming the nonlinear Black-Scholes equation into the diffusion PDE by introducing the log transform of S and (T−t)→τ can provide the most stable platform within which option prices can be evaluated.
Shu-Li Mei
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Regularity results for weak solutions of elliptic PDEs below the natural exponent [PDF]
, 2014 We prove regularity estimates for the weak solutions to the Dirichlet problem for a divergence form elliptic operator.
D. Cruz-Uribe, Kabe Moen, S. Rodney
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Regularity of weak solutions for aclass of elliptic PDEs in Orlicz-Sobolev spaces
Topological Methods in Nonlinear Analysis, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jakub Maksymiuk, Karol Wroński
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