ASYMPTOTIC BEHAVIOR OF THE BLOW-UP AND GLOBAL EXISTENCE FOR A PARABOLIC EQUATION INVOLVING A CRITICAL EXPONENT

DOI10.17654/0975045223002OpenAlexW4313395874MaRDI QIDQ6115114

Kambire Diopina Gnowille, N'Takpe Jean Jacques, Halima Nachid

Publication date: 15 August 2023

Published in: International Journal of Numerical Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.17654/0975045223002

zbMATH Keywords

convergence continuity asymptotic behavior finite difference method blow-up global existence discretizations numerical blow-up time semidiscretizations semi-linear diffusion equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Blow-up in context of PDEs (35B44)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Classification of blow-up with nonlinear diffusion and localized reaction
Semi-discretization in time of a fast diffusion equation
The value of the critical exponent for reaction-diffusion equations in cones
On the critical exponent for reaction-diffusion equations
On the formation of singularities in the critical \(O(3)\) \(\sigma \)-model
Classification of type I and type II behaviors for a supercritical nonlinear heat equation
Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
The critical exponent of degenerate parabolic systems
Critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation. II
On the blow-up time convergence of semidiscretizations of reaction-diffusion equations
Blowup in diffusion equations: A survey
Diffusion models with blow-up
Sharp upper bound on the blow-up rate for the critical nonlinear Schrödinger equation
On critical Fujita exponents for the porous medium equation with a nonlinear boundary condition
The problem of blow-up in nonlinear parabolic equations
On universality of blow up profile for \(L^2\) critical nonlinear Schrödinger equation
On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary
Blow-up for semidiscretizations of reaction-diffusion equations
Type II blow-up for the four dimensional energy critical semi linear heat equation
The role of critical exponents in blow-up theorems: The sequel
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schrödinger equation
Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions
Extinction for discretizations of some semilinear parabolic equations
Blow-Up for Discretization of a Localized Semilinear Heat Equation
Critical exponents for a semilinear parabolic equation with variable reaction
Mathematical Analysis of Thermal Runaway for Spatially Inhomogeneous Reactions
The Role of Critical Exponents in Blowup Theorems
Semidiscretization in Time of Nonlinear Parabolic Equations with Blowup of the Solution
The critical exponents of parabolic equations and blow-up inRⁿ
On the Dependence of the Blow-Up Time with Respect to the Initial Data in a Semilinear Parabolic Problem
On the growth of solutions of quasi‐linear parabolic equations
On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

This page was built for publication: ASYMPTOTIC BEHAVIOR OF THE BLOW-UP AND GLOBAL EXISTENCE FOR A PARABOLIC EQUATION INVOLVING A CRITICAL EXPONENT