Journal ArticleDOI
Blow-up at the boundary for degenerate semilinear parabolic equations
TLDR
In this article, it was shown that for a large class of initial data, blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic.Abstract:
This paper treats a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover, it is proved that for a large class of initial data, blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The mathematical analysis is then extended to equations with other degeneracies.read more
Citations
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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.
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Moving Mesh Methods for Problems with Blow-up
TL;DR: This paper considers moving mesh methods for which the mesh is determined using so-called moving mesh partial differential equations (MMPDEs), and it is shown that for suitable ones the MMPDE solution evolves towards a (moving) mesh which close to the blow-up point automatically places the mesh points in such a manner that the ignition kernel approaches a constant as $t\to T$ (theblow-up time).
Journal Article
Decay estimates of heat transfer to melton polymer flow in pipes with viscous dissipation
Dongming Wei,Zhengbu Zhang +1 more
TL;DR: In this article, the authors compare a parabolic equation with an elliptic equation and derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance.
Journal ArticleDOI
On the computation of blow-up
TL;DR: In this article, a class of time-stepping strategies that correspond to a time-continuous re-scaling of the underlying differential equation is proposed; this class is analyzed and criteria established to determine suitable choices for the rescaling.
Journal ArticleDOI
Critical Fujita exponents of degenerate and singular parabolic equations
Chunpeng Wang,Si Ning Zheng +1 more
TL;DR: In this paper, the authors investigated the critical Fujita exponent for the initial value problem of the degenerate and singular nonlinear parabolic equation with a non-negative initial value.
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Linear and Quasilinear Equations of Parabolic Type
TL;DR: In this article, the authors considered a hyperbolic parabolic singular perturbation problem for a quasilinear equation of kirchhoff type and obtained parameter dependent time decay estimates of the difference between the solutions of the solution of a quasi-linear parabolic equation and the corresponding linear parabolic equations.
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
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Channel flow with temperature-dependent viscosity and internal viscous dissipation
TL;DR: In this paper, the authors used asymptotic methods to analyse the flow in a narrow channel of a fluid with temperature-dependent viscosity and internal viscous dissipation.