Results 21 to 30 of about 87,102,086 (248)
Regularity for quasilinear PDEs in Carnot groups via Riemannian approximation
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of weak solutions to subelliptic quasilinear PDEs in Carnot groups of the formΣi=1m1Xi (Φ(|∇Hu|2)Xiu) = 0. Here ∇Hu = (X1u,...,Xmiu) is the horizontal gradient, δ > 0 and the exponent p ∈ [2, p*), where p* depends on ...
András Domokos, Juan J. Manfredi
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Weak solutions of quasilinear elliptic PDE's at resonance [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 1997 The authors study a class of variational quasilinear elliptic PDE's with resonance at infinity. The proof of their existence results are based on a new generalization to continuous functionals of the saddle point theorem and of a multiplicity result.
ARIOLI, GIANNI, GAZZOLA, FILIPPO
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Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning [PDF]
SIAM Journal on Scientific Computing, 2020 This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via Friedrichs' seminal minimax formulation, which transforms the PDE problem into a minimax optimization problem to identify weak ...
Fan Chen +3 more
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wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws [PDF]
arXiv.org, 2022 Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic equations.
Tim De Ryck +2 more
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LONG TIME BEHAVIOR OF THE SOLUTIONS OF NLW ON THE $d$-DIMENSIONAL TORUS
Forum of Mathematics, Sigma, 2020 We consider the nonlinear wave equation (NLW) on the $d$-dimensional torus $\mathbb{T}^{d}$ with a smooth nonlinearity of order at least 2 at the origin. We prove that, for almost any mass, small and smooth solutions of high Sobolev indices are stable up
JOACKIM BERNIER +2 more
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Nonlinear Analysis: Real world applications, 2022 We consider a system of PDEs describing a non-homogeneous, non-Newtonian and incompressible fluid in a space-periodic domain. We define the generalized dissipative weak solutions as well as give a proof of its existence, when the boundary data is ...
Jakub Woźnicki
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Boundedness of Wolff-type potentials and applications to PDEs [PDF]
Nonlinear Analysis: Real world applications, 2022 We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle for that integral operators, that is, a characterization of those ...
Micha l Borowski +2 more
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Existence of weak solutions to nonlocal PDEs with a generalized definition of Caputo derivative
, 2022 Some compactness criteria that are analogies of the Aubin–Lions lemma for the existence of weak solutions of nonlinear evolutionary PDEs play crucial roles for the existence of weak solutions to time-fractional PDEs. Based on this fact, in this paper, we
Xu, Jiaohui, Caraballo Garrido, Tomás
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Stochastic PDEs with multiscale structure [PDF]
, 2012 We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise.
Martin Hairer +3 more
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Convergence of hyperbolic approximations to higher-order PDEs for smooth solutions [PDF]
SMAI Journal of Computational MathematicsWe prove the convergence of hyperbolic approximations for several classes of higher-order PDEs, including the Benjamin–Bona–Mahony, Korteweg–de Vries, Gardner, Kawahara, and Kuramoto–Sivashinsky equations, provided a smooth solution of the limiting ...
Jan Giesselmann, Hendrik Ranocha
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