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Page 3355 of Mathematical Reviews Vol. , Issue 92f
[page]
1992
Mathematical Reviews
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For fixed parameter values and arbitrarily fine discretizations we construct solutions which blow up in finite time for two semi- discrete schemes. ...
This connection between the blow-up phenome- non and spurious steady states is also explored for Galerkin and nonlinear Galerkin semi-discrete approximations. ...
Page 4063 of Mathematical Reviews Vol. , Issue 2004e
[page]
2004
Mathematical Reviews
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An initial-boundary value problem for a semilinear parabolic equa- tion with parameter ¢~? in front of the nonlinear reaction term is considered. ...
(RA-UBAS; Buenos Aires)
Adaptive numerical schemes for a parabolic problem with blow-up. (English summary)
IMA J. Numer. Anal. 23 (2003), no. 3, 439-463. ...
Page 6126 of Mathematical Reviews Vol. , Issue 97J
[page]
1997
Mathematical Reviews
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In this paper the authors consider a semi-implicit discretization of a scalar one-dimensional parabolic equation of the form u, = ux. + f(u) with homogeneous Dirichlet boundary conditions in [0, 1]. ...
Carvalho (BR-SPL3-IC; Sado Carlos)
97j:35080 35K60 35840
Yang, Shi Xin (PRC-XIAM; Xiamen)
Extinction of solutions of semilinear heat equations with a gradient term. (Chinese. ...
Page 5483 of Mathematical Reviews Vol. , Issue 2001H
[page]
2001
Mathematical Reviews
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The paper deals with the large-time behaviour of sign-changing solutions of inhomogeneous parabolic equations and systems. ...
The well-posedness of this problem was already studied by the authors. Let up be a solution of the initial-boundary value problem without source term. ...
Page 1049 of Mathematical Reviews Vol. , Issue 2004b
[page]
2004
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1049 35K Parabolic equations and systems
priate hypotheses, we establish the local existence and uniqueness of a positive classical solution and obtain that the solution either exists globally or blows ...
A weakly coupled system of parabolic equations
8,u'?) ...
Page 6123 of Mathematical Reviews Vol. , Issue 99i
[page]
1999
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Qing Fang (J-EHIMSS; Matsuyama)
991:35066 35K55 35B05 Zaag, Hatem (F-ENS-MI; Paris) Blow-up results for vector-valued nonlinear heat equations with no gradient structure. (English summary) Ann. Inst. ...
The reaction-diffusion equation u, = Au + (i+ id)|u\?~'u, ue, is considered. The author proves existence of a blow-up solution for small 6 and suitable initial data up. ...
Page 3348 of Mathematical Reviews Vol. , Issue 95f
[page]
1995
Mathematical Reviews
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A 8 (1993), no. 4, 351-359.
Summary: “The blow-up of the solutions to initial-boundary value problems for a class of nonlinear pseudohyperbolic equations u,, — Uxx = au? ...
Nguyén Hong Thai (PL-SZCZ; Szczecin)
95:35030 35B40 35B05 35L70
Yang, Zhi Jian
Blow-up of solutions to initial-boundary value problems for a class
of nonlinear evolution equations. (Chinese. ...
Parabolic Monge–Ampère methods for blow-up problems in several spatial dimensions
2006
Journal of Physics A: Mathematical and General
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The scheme is based on computing a Legendre transformation from a regular to a spatially non-uniform mesh via the solution of a relaxed form of the Monge-Ampere equation. ...
Numerical examples are presented in one and two dimensions which demonstrate the effectiveness of this approach. ...
The map from computational to physical coordinates is determined in terms of the gradient of a mesh potential Q which satisfies a parabolic partial differential equation. ...
doi:10.1088/0305-4470/39/19/s06
fatcat:6ykzsga5bnhwfdrymgebjrwdgy
Refined blow-up asymptotics for a perturbed nonlinear heat equation with a gradient and a non-local term
[article]
2021
arXiv
pre-print
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We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. ...
In some earlier works [1, 2], we constructed a solution u for that equation such that u and ∇ u both blow up at the origin and only there. We also gave the final blow-up profile. ...
Zaag, Construction of a blow-up solution for a perturbed
nonlinear heat equation with a gradient term, J. Differential Equations, 272
(2021) 1-45.
[2] B. Abdelhedi and H. ...
arXiv:2112.03039v1
fatcat:zhew4vze5bdchotmb23iu3kxnu
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
[article]
2016
arXiv
pre-print
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We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonlinear solver. ...
With extensive numerical tests, we verify the claimed properties of the methods and demonstrate their superiority in various challenging applications. ...
The initial condition is taken the same as in
Blow up In this subsection, we focus on the cases when ρ blows up, and show that our schemes, (4.8) In Fig. 5 on the left, we plot a slice of solution ...
arXiv:1610.03016v2
fatcat:g3mvrzk6qze4hlbvifecwukrsq
Numerical simulation of nonlinear continuity equations by evolving diffeomorphisms
2016
Journal of Computational Physics
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Positivity of solutions as well as energy decrease of the semi-discrete scheme are guaranteed by its construction. We illustrate this properties with various examples in spatial dimension one and two. ...
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance ...
Acknowledgments JAC was partially supported by the Royal Society via a Wolfson Research Merit Award. ...
doi:10.1016/j.jcp.2016.09.040
fatcat:y7hymheapjdh7jl73gk6chbiii
author index volume
2007
Journal of Computational and Applied Mathematics
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Vulkov, Blow-up of continuous and semidiscrete solutions to elliptic equations with semilinear dynamical boundary conditions of parabolic type 414-434 Koulaei, M.H. and F. ...
matrices 258-265 Du, L., Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources 237-247 Gegenhasi see Wang, H. ...
doi:10.1016/s0377-0427(07)00064-7
fatcat:32gvtji2gvf5lfvlq74xjnkpsi
Convergence of a Semi-Discrete Numerical Method for a Class of Nonlocal Nonlinear Wave Equations
[article]
2018
arXiv
pre-print
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In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution ...
Finally, we present some numerical experiments that confirm numerically both the expected convergence rate of the semi-discrete scheme and the ability of the method to capture finite-time blow-up of solutions ...
blow-up of solutions. ...
arXiv:1805.07264v1
fatcat:ccutdizbybadpjongbxyrb4fiu
Convergence of a semi-discrete numerical method for a class of nonlocal nonlinear wave equations
2018
Mathematical Modelling and Numerical Analysis
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In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution ...
Finally, we present some numerical experiments that confirm numerically both the expected convergence rate of the semi-discrete scheme and the ability of the method to capture finite-time blow-up of solutions ...
blow-up of solutions. ...
doi:10.1051/m2an/2018035
fatcat:2qrfatubljbxhnpupu4vvrcyeq
Page 1134 of Mathematical Reviews Vol. , Issue 2000b
[page]
2000
Mathematical Reviews
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Blowing-up of solutions for a class of higher-order reaction-diffusion equations. (Chinese. English and Chinese summaries)
Math. Practice Theory 28 (1998), no. 3, 220-225. ...
Sufficient conditions for blow-up of solutions for the two systems are obtained. ...
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