Bounds for blow-up time in nonlinear parabolic problems
نویسندگان
چکیده
منابع مشابه
Bounds for blow-up time in nonlinear parabolic problems
A first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow-up time in initial-boundary value problems for parabolic equations of the form ut = div ( ρ(u)gradu )+ f (u) if blow-up occurs. In addition, conditions which ensure that blow-up occurs or does not occur are presented. © 2007 Elsevier Inc. All rights reserved.
متن کاملBlow-up in the Parabolic Problems under Nonlinear Boundary Conditions
In this paper, I consider nonlinear parabolic problems under nonlinear boundary conditions. I establish respectively the conditions on nonlinearities to guarantee that ( , ) u x t exists globally or blows up at some finite time. If blow-up occurs, an upper bound for the blow-up time is derived, under somewhat more restrictive conditions, lower bounds for the blow-up time are also derived.
متن کاملBlow-up Results for Nonlinear Parabolic Equations on Manifolds
1. Introduction. The aim of this paper is threefold. First, by a unified approach, we prove that several classical blow-up results obtained over the last three decades for semilinear and quasilinear parabolic problems in R n are valid on noncompact, complete Riemannian manifolds, which include those with nonnegative Ricci curvatures. Next, we remove some unnecessary a priori growth conditions o...
متن کاملBlow-up properties for parabolic systems with localized nonlinear sources
This paper deals with blow-up properties of solutions to a semilinear parabolic system with nonlinear localized source involved a product with local terms ut = Δu+ exp{mu(x,t)+nv(x0 ,t)}, vt = Δv+ exp{pu(x0,t)+qv(x,t)} with homogeneous Dirichlet boundary conditions. We investigate the influence of localized sources and local terms on blow-up properties for this system, and prove that: (i) when ...
متن کاملBlow-up for Parabolic and Hyperbolic Problems with Variable Exponents
In this paper we study the blow up problem for positive solutions of parabolic and hyperbolic problems with reaction terms of local and nonlocal type involving a variable exponent. We prove the existence of initial data such that the corresponding solutions blow up at a finite time.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2008
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2007.05.022