Journal ArticleDOI
A rescaling algorithm for the numerical calculation of blowing-up solutions
Marsha Berger,Robert V. Kohn +1 more
TLDR
In this article, the authors present an invariance d'echelle for le calcul numerique des solutions a singularites explosives des equations d'evolution non lineaires, i.e.Abstract:
On presente un algorithme a invariance d'echelle pour le calcul numerique des solutions a singularites explosives des equations d'evolution non lineairesread more
Citations
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Book
Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
Journal ArticleDOI
The role of critical exponents in blowup theorems
TL;DR: In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation u_t =Delta u + u^p in $R^N with nonnegative initial values.
Journal ArticleDOI
Nondegeneracy of blowup for semilinear heat equations
Yoshikazu Giga,Robert V. Kohn +1 more
Journal ArticleDOI
Adaptivity with moving grids
TL;DR: R-adaptive methods have enormous potential and indeed can produce an optimal form of adaptivity for many problems, including scale-invariant problems, blow-up problems, problems with moving fronts and problems in meteorology.
References
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Journal ArticleDOI
Asymptotically self‐similar blow‐up of semilinear heat equations
Yoshikazu Giga,Robert V. Kohn +1 more
TL;DR: In this paper, the authors studied the blow-up of solutions of a nonlinear heat equation and characterized the asymptotic behavior of u near a singularity, assuming a suitable upper bound on the rate of blowup.
Journal Article
Blow-up of positive solutions of semilinear heat equations
TL;DR: On considere le probleme aux valeurs limites et initiales: u t =Δu+f(u) dans Ω×(0,T), u(x,0) =Φ(x) si x∈Ω, u(X,t)=0 si x ∈∂Ω and o
Journal Article
Characterizing Blow-up Using Similarity Variables
Yoshikazu Giga,Robert V. Kohn +1 more
Journal ArticleDOI
A nonlinear instability burst in plane parallel flow
TL;DR: In this article, an infinitesimal centre disturbance is imposed on a fully developed plane Poiseuille flow at a Reynolds number R slightly greater than the critical value Rc for instability, and it is shown numerically and confirmed analytically that for a finite value of (R-Rc)t, the amplitude A develops an infinite peak at the wave centre.
Journal ArticleDOI
Estimates of intermittency, spectra, and blow-up in developed turbulence
TL;DR: In this paper, a two-week l oan copy of the book is provided for two weeks, which may be borrowed for a period of two weeks for a personal retention copy.
Related Papers (5)
Asymptotically self‐similar blow‐up of semilinear heat equations
Yoshikazu Giga,Robert V. Kohn +1 more