scholarly journals On the effect of higher order derivatives of initial data on the blow-up set for a semilinear heat equation

2018 ◽  
Vol 17 (2) ◽  
pp. 449-475 ◽  
Author(s):  
Yohei Fujishima ◽  
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Blow Up ◽  
Higher Order ◽  
Semilinear Heat Equation ◽  
Derivatives Of

Global Sign-changing Solutions of a Higher Order Semilinear Heat Equation in the Subcritical Fujita Range

2012 ◽  
Vol 12 (3) ◽  
Author(s):  
Victor A. Galaktionov ◽  
Enzo Mitidieri ◽  
Stanislav I. Pohozaev
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Initial Function ◽  
Blow Up ◽  
Higher Order ◽  
Semilinear Heat Equation ◽  
Sign Changing Solutions

AbstractA detailed study of two classes of oscillatory global (and blow-up) solutions was began in [20] for the semilinear heat equation in the subcritical Fujita rangewith bounded integrable initial data u(x, 0) = uwith the same initial data u∫ ui.e., as for (0.1), any such arbitrarily small initial function u

scholarly journals Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation

1996 ◽  
Vol 39 (1) ◽  
pp. 81-96
Author(s):  
D. E. Tzanetis
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Asymptotic Behaviour ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Heat Equation ◽  
Unbounded Solutions ◽  
Semilinear Heat Equation ◽  
Initial Boundary Value

The initial-boundary value problem for the nonlinear heat equation u1 = Δu + λf(u) might possibly have global classical unbounded solutions, for some “critical” initial data . The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x;λ) for some values of λ We find, for radial symmetric solutions, that u*(r, t)→w(r) for any 0<r≤l but supu*(·, t) = u*(0, t)→∞, as t→∞. Furthermore, if , where is some such critical initial data, then û = u(x, t; û0) blows up in finite time provided that f grows sufficiently fast.

Classification of Global and Blow-up Sign-changing Solutions of a Semilinear Heat Equation in the Subcritical Fujita Range : Second-order Diffusion

2014 ◽  
Vol 14 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Victor A. Galaktionov ◽  
Enzo Mitidieri ◽  
Stanislav I. Pohozaev
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Blow Up ◽  
Second Order ◽  
Seminal Paper ◽  
Semilinear Heat Equation ◽  
Sign Changing Solutions

AbstractIt is well known from the seminal paper by Fujita [22] for 1 < p < puwith arbitrary initial data u

scholarly journals Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data

2018 ◽  
Vol 144 (3) ◽  
pp. 287-297
Author(s):  
Amy Poh Ai Ling ◽  
Masahiko Shimojō
Keyword(s):  
Initial Data ◽  
Heat Equation ◽  
Blow Up ◽  
Slow Diffusion

scholarly journals Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

2019 ◽  
Vol 53 (1) ◽  
pp. 57-72
Author(s):  
Marcos Josías Ceballos-Lira ◽  
Aroldo Pérez
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Mild Solution ◽  
Blow Up ◽  
Local Existence ◽  
Dirichlet Condition ◽  
Infinite Time ◽  
Diffusion Operator ◽  
Intrinsic Ultracontractivity ◽  
Semilinear Heat Equation

In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

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