scholarly journals On the blow-up of a non-local parabolic problem

2006 ◽  
Vol 19 (9) ◽  
pp. 921-925 ◽  
Author(s):  
N.I. Kavallaris ◽  
D.E. Tzanetis
Keyword(s):  
Parabolic Problem ◽  
Blow Up ◽  
Non Local

scholarly journals Finite-time blow-up of a non-local stochastic parabolic problem

2020 ◽  
Vol 130 (9) ◽  
pp. 5605-5635
Author(s):  
Nikos I. Kavallaris ◽  
Yubin Yan
Keyword(s):  
Finite Time ◽  
Parabolic Problem ◽  
Blow Up ◽  
Non Local

Estimates of blow-up time for a non-local problem modelling an Ohmic heating process

2002 ◽  
Vol 13 (3) ◽  
pp. 337-351 ◽  
Author(s):  
N. I. KAVALLARIS ◽  
C. V. NIKOLOPOULOS ◽  
D. E. TZANETIS
Keyword(s):  
Blow Up ◽  
Ohmic Heating ◽  
Numerical Estimate ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stationary Solutions ◽  
Upper And Lower Bounds ◽  
Heating Process ◽  
Non Local ◽  
Initial Boundary Value

We consider an initial boundary value problem for the non-local equation, ut = uxx+λf(u)/(∫1-1f (u)dx)2, with Robin boundary conditions. It is known that there exists a critical value of the parameter λ, say λ*, such that for λ > λ* there is no stationary solution and the solution u(x, t) blows up globally in finite time t*, while for λ < λ* there exist stationary solutions. We find, for decreasing f and for λ > λ*, upper and lower bounds for t*, by using comparison methods. For f(u) = e−u, we give an asymptotic estimate: t* ∼ tu(λ−λ*)−1/2 for 0 < (λ−λ*) [Lt ] 1, where tu is a constant. A numerical estimate is obtained using a Crank-Nicolson scheme.

Sign in / Sign up

Export Citation Format

Share Document