scholarly journals On global existence and bounds for blow-up time in nonlinear parabolic problems with time dependent coefficients

2013 ◽  
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Time Dependent ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic

scholarly journals Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lingling Zhang ◽  
Hui Wang
Keyword(s):  
Global Solution ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Parabolic Problems ◽  
Maximum Principles ◽  
Gradient Term ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Robin Boundary ◽  
Upper Estimate

We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions:(b(u))t=∇·(h(t)k(x)a(u)∇u)+f(x,u,|∇u|2,t), inD×(0,T),(∂u/∂n)+γu=0, on∂D×(0,T),u(x,0)=u0(x)>0, inD¯, whereD⊂RN  (N≥2)is a bounded domain with smooth boundary∂D. Under some appropriate assumption on the functionsf,h,k,b, andaand initial valueu0, we obtain the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for “blow-up time,” and an upper estimate of “blow-up rate.” Our approach depends heavily on the maximum principles.

Blow-up phenomena for some nonlinear parabolic problems

2008 ◽  
Vol 69 (10) ◽  
pp. 3495-3502 ◽  
Author(s):  
L.E. Payne ◽  
G.A. Philippin ◽  
P.W. Schaefer
Keyword(s):  
Blow Up ◽  
Parabolic Problems ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic

Blow-up Results for Parabolic Inequalities with Chipot–Weissler Nonlinearity in the Gradient Term

2004 ◽  
Vol 4 (2) ◽  
Author(s):  
Anna Maria Piccirillo ◽  
Luisa Toscano ◽  
Speranza Toscano
Keyword(s):  
Positive Solutions ◽  
Wide Class ◽  
Blow Up ◽  
Parabolic Problems ◽  
Gradient Term ◽  
Nonlinear Parabolic Problems ◽  
Nonlinear Parabolic ◽  
Open Question ◽  
Parabolic Inequalities

AbstractWe obtain blow-up results for a wide class of nonlinear parabolic problems with nonlinearity of the Chipot-Weissler type in the gradient term. Some of these answer an open question concerning the nonexistence of positive solutions to the problemwhere λ > 0 is small, u

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