Special issue on degenerate and singular PDEs and phenomena in analysis and mathematical physics
Journal of Mathematical Analysis and Applications, 2009 Vicenţiu D. Rădulescu
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Decay Estimates for 1-D Parabolic PDEs with Boundary Disturbances [PDF]
, 2017 In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the L2 and H1 norms of the solution and discontinuous disturbances
Karafyllis, Iasson, Krstic, Miroslav
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A class of second-order geometric quasilinear hyperbolic PDEs and their application in imaging science [PDF]
, 2019 In this paper, we study damped second-order dynamics, which are quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems for accelerating energy decay of gradient flows.
Dong, Guozhi +2 more
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Weak Continuity and Compactness for Nonlinear Partial Differential Equations [PDF]
, 2015 We present several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role.
Chen, Gui-Qiang G.
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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 ...
AV Knyazev +24 more
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IGA-based Multi-Index Stochastic Collocation for random PDEs on arbitrary domains
, 2019 This paper proposes an extension of the Multi-Index Stochastic Collocation (MISC) method for forward uncertainty quantification (UQ) problems in computational domains of shape other than a square or cube, by exploiting isogeometric analysis (IGA ...
Beck, Joakim +2 more
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A mixed $\ell_1$ regularization approach for sparse simultaneous approximation of parameterized PDEs
, 2018 We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs.
Dexter, Nick +2 more
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Analysis of Schwarz methods for a hybridizable discontinuous Galerkin discretization: The many-subdomain case [PDF]
Mathematics of Computation, 2016 Schwarz methods are attractive parallel solution techniques for solving large-scale linear systems obtained from discretizations of partial differential equations (PDEs).
M. Gander, Soheil Hajian
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Additive domain decomposition operator splittings -- convergence analyses in a dissipative framework
, 2016 We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems.
Hansen, Eskil, Henningsson, Erik
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