Results 51 to 60 of about 8,306 (123)

Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach

, 2009
Five types of blow-up patterns that can occur for the 4th-order semilinear parabolic equation of reaction-diffusion type $$ u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1, \quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, $
Bakirova M I, Bebernes J, Bricmont J, Dalmasso R, Dold J W, Egorov Yu V, Fefferman C, Frank-Kamenetskii D A, Frank-Kamenetskii D A, Galaktinov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Galaktionov V A, Guo Y, Hamilton R, Herrero M A, Herrero M A, Ibragimov N H, Joulin G Mikishev A B Sivashinsky G I, Kato T, Kurdyumov S P, Kurdyumov S P, Lepin L A, Lepin L A, Leray J, Levitan B M, Loewner C, Lunardi A, Maz'ja V, Mitidieri E, Naimark M A, Nussair E S, Ovsiannikov L V, Pao C V, Peletier L A, Quittner P, Samarskii A A, Semenov N, Svirshchevskii S R, Svirshchevskii S R, Tao T, V A Galaktionov, Velazquez J J L, Zel'dovich Ya B   +52 more
core   +2 more sources

Robust Inverse Material Design With Physical Guarantees Using the Voigt‐Reuss Net

International Journal for Numerical Methods in Engineering, Volume 127, Issue 7, 15 April 2026.
ABSTRACT We apply the Voigt‐Reuss net, a spectrally normalized neural surrogate introduced in [38], for forward and inverse mechanical homogenization with a key guarantee that all predicted effective stiffness tensors satisfy Voigt‐Reuss bounds in the Löwner sense during training, inference, and gradient‐driven optimization.
Sanath Keshav, Felix Fritzen
wiley   +1 more source

Complex singularities and PDEs

, 2015
In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum.
Caflisch, R. E., Gargano, F., Sammartino, M., Sciacca, V.   +3 more
core  

A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations. [PDF]

Entropy (Basel), 2023
Sun K, Feng X.
europepmc   +1 more source

Current progress toward isogeometric modeling of the heart biophysics. [PDF]

Biophys Rev (Melville), 2023
Torre M, Morganti S, Pasqualini FS, Reali A.   +3 more
europepmc   +1 more source

Fast automated adjoints for spectral PDE solvers. [PDF]

Proc Natl Acad Sci U S A
Skene CS, Burns KJ.
europepmc   +1 more source

A neural network-based PDE solving algorithm with high precision. [PDF]

Sci Rep, 2023
Jiang Z, Jiang J, Yao Q, Yang G.
europepmc   +1 more source

Analytical evaluations using neural network-based method for wave solutions of combined Kairat-II-X differential equation in fluid mechanics. [PDF]

Sci Rep
Zhou P, Manafian J, Lakestani M, Ilhan OA, Bahador NJ, Fattah AA, Mahmoud KH, Nuray R, Nagiyeva N.   +8 more
europepmc   +1 more source

Entropy in Exact 2D Navier-Stokes and 3D Burgers Gas Flows. [PDF]

Entropy (Basel)
Broadbridge P.
europepmc   +1 more source

Physics-Informed Neural Networks with Unknown Partial Differential Equations: An Application in Multivariate Time Series. [PDF]

Entropy (Basel)
Mortezanejad SAF, Wang R, Mohammad-Djafari A.   +2 more
europepmc   +1 more source