Zobrazeno 1 - 10
of 20
pro vyhledávání: '"Ujjwal Koley"'
Publikováno v:
Journal of Computational Mathematics. 39:816-847
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm andBenjamin-Ono equations. The stability of solutions of these di
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b385c6787c18e18563d751d6ba0b29b4
https://doi.org/10.4208/jcm.2101-m2020-0342
https://doi.org/10.4208/jcm.2101-m2020-0342
Publikováno v:
SIAM/ASA Journal on Uncertainty Quantification. 9:65-105
We establish a notion of random entropy solution for degenerate fractional conservation laws incorporating randomness in the initial data, convective flux, and diffusive flux. In order to quantify ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::961b3fe2055c3f96f457b7063b6ea041
https://doi.org/10.1137/19m1279447
https://doi.org/10.1137/19m1279447
Publikováno v:
Stochastic Processes and their Applications
Stochastic Processes and their Applications, Elsevier, 2020, 130 (9), pp.5310-5365. ⟨10.1016/j.spa.2020.03.009⟩
Stochastic Processes and their Applications, Elsevier, 2020, 130 (9), pp.5310-5365. ⟨10.1016/j.spa.2020.03.009⟩
In this article, we explore some of the main mathematical problems connected to multidimensional fractional conservation laws driven by Levy processes. Making use of an adapted entropy formulation, a result of existence and uniqueness of a solution i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88f95ff6717276c766d59e23a3e18cee
https://hal.archives-ouvertes.fr/hal-03125104
https://hal.archives-ouvertes.fr/hal-03125104
We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operat
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ed74cb70cf450b553a236f738414bcf4
http://arxiv.org/abs/2008.03141
http://arxiv.org/abs/2008.03141
Autor:
Abhishek Chaudhary, Ujjwal Koley
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure and a concen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df3d92b0cdce1af3de753ff96c65624c
Autor:
Ujjwal Koley, Peder Aursand
Publikováno v:
Journal of Computational and Applied Mathematics. 317:478-499
We consider a nonlinear variational wave equation that models the dynamics of nematic liquid crystals. Discontinuous Galerkin schemes that either conserve or dissipate a discrete version of the energy associated with these equations are designed. Num
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e4b24516607b57130dfb7d91240e2b19
https://doi.org/10.1016/j.cam.2016.12.006
https://doi.org/10.1016/j.cam.2016.12.006
Publikováno v:
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2018, 38 (2), pp.998-1050. ⟨10.1093/imanum/drx023⟩
IMA Journal of Numerical Analysis, Oxford University Press (OUP), 2018, 38 (2), pp.998-1050. ⟨10.1093/imanum/drx023⟩
In this paper, we analyze a semi-discrete finite difference scheme for a conservation laws driven by a homogeneous multiplicative Levy noise. Thanks to BV estimates, we show a compact sequence of approximate solutions, generated by the finite differe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77c620e325b0aef4cb79c904c12b86d8
https://hal.archives-ouvertes.fr/hal-02134602
https://hal.archives-ouvertes.fr/hal-02134602
Publikováno v:
Numerische Mathematik. 134:249-274
In this paper, we analyze finite difference schemes for Benjamin---Ono equation, $$u_t= u u_x + H u_{xx}$$ut=uux+Huxx, where H denotes the Hilbert transform. Both the decaying case on the full line and the periodic case are considered. If the initial
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::198c2453cfbd71529ae23dcaf3534c0d
https://doi.org/10.1007/s00211-015-0778-6
https://doi.org/10.1007/s00211-015-0778-6
Publikováno v:
Journal of Differential Equations. 259:4683-4706
We are concerned with multidimensional stochastic balance laws driven by Levy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the nonlinearities of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::955fe34ec1ba3fe280c56f5133fed148
https://doi.org/10.1016/j.jde.2015.06.024
https://doi.org/10.1016/j.jde.2015.06.024
Publikováno v:
Acta Mathematica Scientia. 35:281-302
We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2cd9115a92a2431868ded5f7213c0c95
https://doi.org/10.1016/s0252-9602(15)60001-7
https://doi.org/10.1016/s0252-9602(15)60001-7