scholarly journals The porous medium equation with large initial data on negatively curved Riemannian manifolds

2018 ◽  
Vol 113 ◽  
pp. 195-226 ◽  
Author(s):  
Gabriele Grillo ◽  
Matteo Muratori ◽  
Fabio Punzo
Keyword(s):  
Porous Medium ◽  
Initial Data ◽  
Riemannian Manifolds ◽  
Porous Medium Equation ◽  
Large Initial Data ◽  
Negatively Curved ◽  
Medium Equation

Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison

1985 ◽  
Vol 100 (1-2) ◽  
pp. 1-10
Author(s):  
Nicholas D. Alikakos ◽  
Rouben Rostamian
Keyword(s):  
Porous Medium ◽  
Initial Data ◽  
Original Problem ◽  
Large Time ◽  
Porous Medium Equation ◽  
Comparison Method ◽  
Upper And Lower Bounds ◽  
Medium Equation ◽  
Time Estimates ◽  
The Cauchy Problem

SynopsisWe consider the Cauchy problem for the porous medium equation in one space dimension, with initial data which are locally integrable. We measure the asymptotic behaviour of the initial data near infinity in an integral sense and relate this to the pointwise rate of growth or decay of solution for large time. The emphasis is on a novel comparison method wherein the initial data are rearranged on the ×-axis to form a sequence of Dirac δ-masses. By using the explicit solution in the latter case, we derive upper and lower bounds for the solution to the original problem by comparisons.

Existence and blow-up of solutions for a non-local filtration and porous medium problem

2010 ◽  
Vol 53 (1) ◽  
pp. 195-209 ◽  
Author(s):  
E. A. Latos ◽  
D. E. Tzanetis
Keyword(s):  
Porous Medium ◽  
Initial Data ◽  
Blow Up ◽  
Porous Medium Equation ◽  
Filtration Equation ◽  
Medium Equation ◽  
Non Local ◽  
Image Position

AbstractWe consider a non-local filtration equation of the formand a porous medium equation, in this case K(u) = um, with some boundary and initial data u0, where 0 < p < 1 and f, f′, f″ > 0. We prove blow-up of solutions for sufficiently large values of the parameter λ > 0 and for any u0 > 0, or for sufficiently large values of u0 > 0 and for any λ λ 0.

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