Results 21 to 30 of about 304,931 (226)

Blow-up for a degenerate and singular parabolic equation with a nonlocal source

Advances in Difference Equations, 2019
This article studies the blow-up phenomenon for a degenerate and singular parabolic problem. Conditions for the local and global existence of solutions for the problem are given.
Nitithorn Sukwong, Panumart Sawangtong, Sanoe Koonprasert, Wannika Sawangtong   +3 more
doaj   +1 more source

Finite-time blowup for a complex Ginzburg-Landau equation [PDF]

, 2012
We prove that negative energy solutions of the complex Ginzburg-Landau equation $e^{-i\theta} u_t = \Delta u+ |u|^{\alpha} u$ blow up in finite time, where \alpha >0 and \pi ...
Caffarelli L., Flávio Dickstein, Fred B. Weissler, Kato T., Kavian O., Levermore C.D., Ogawa T., Thierry Cazenave, Zakharov V.E.   +8 more
core   +4 more sources

Refined Regularity of the Blow-Up Set Linked to Refined Asymptotic Behavior for the Semilinear Heat Equation

Advanced Nonlinear Studies, 2017
We consider u⁢(x,t)${u(x,t)}$, a solution of ∂t⁡u=Δ⁢u+|u|p-1⁢u${\partial_{t}u=\Delta u+|u|^{p-1}u}$ which blows up at some time T>0${T>0}$, where u:ℝN×[0,T)→ℝ${u:\mathbb{R}^{N}\times[0,T)\to\mathbb{R}}$, p>1${p>1}$ and (N-2)⁢p0}$.
Ghoul Tej-Eddine, Nguyen Van Tien, Zaag Hatem   +2 more
doaj   +1 more source

Theoretical and numerical studies of the blow-up of a degenerate nonlinear reaction–diffusion problem with source terms

Applied Mathematics in Science and Engineering
In this paper, we focus on the phenomenon of blow-up of solutions for semilinear and degenerate (time-derivative) parabolic equation systems with additional source terms.
Bariza Sidhoum, Nadjat Doudi, Lamine Nisse, Asma Alharbi, Salah Boulaaras   +4 more
doaj   +1 more source

The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation

Boundary Value Problems, 2020
The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations.
Yuanfei Li, Lianhong Guo, Peng Zeng
doaj   +1 more source

Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions

, 2014
We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\mathbb R^d\to S^d$. For each dimension $d>2+k(2+2\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched asymptotics by glueing a
Biernat, Paweł
core   +1 more source

Boundary blow-up solutions with a spike layer

Journal of Differential Equations, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Du, Yihong, Yan, Shusen
openaire   +2 more sources

Global and blow-up solutions for a nonlinear reaction diffusion equation with Robin boundary conditions

Boundary Value Problems, 2020
In the paper, we investigate global and blow-up solutions for a class of nonlinear reaction diffusion equations with Robin boundary conditions. By using auxiliary functions and a first-order differential inequality technique, we establish conditions on ...
Huimin Tian, Lingling Zhang
doaj   +1 more source

The Blow-Up of the Local Energy Solution to the Wave Equation with a Nontrivial Boundary Condition

Mathematics
In this study, we examine the wave equation with a nontrivial boundary condition. The main target of this study is to prove the local-in-time existence and the blow-up in finite time of the energy solution.
Yulong Liu
doaj   +1 more source

Blow-Up Solution of Modified-Logistic-Diffusion Equation

International Journal of Differential Equations, 2019
Modified-Logistic-Diffusion Equation ut=Duxx+u|1-u| with Neumann boundary condition has a global solution, if the given initial condition ψ satisfies ψ(x)≤1, for all x∈[0,1].
P. Sitompul, Y. Soeharyadi
doaj   +1 more source