sobolev problem
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2020 ◽  
Vol 487 (1) ◽  
pp. 123926
Author(s):  
Asma Benhamida ◽  
Habib Yazidi
Keyword(s):  


2017 ◽  
Vol 97 (14) ◽  
pp. 2544-2553
Author(s):  
Rejeb Hadiji ◽  
Sami Baraket ◽  
Habib Yazidi
Keyword(s):  


2016 ◽  
Vol 442 (2) ◽  
pp. 451-468 ◽  
Author(s):  
M.O. Korpusov ◽  
D.V. Lukyanenko ◽  
A.A. Panin ◽  
E.V. Yushkov


2011 ◽  
Vol 13 (05) ◽  
pp. 843-862 ◽  
Author(s):  
ADIMURTHI ◽  
NGONN SEAM ◽  
GUY VALLET

In this paper, we are interested in the following pseudoparabolic problem, known as the Barenblatt–Sobolev problem: f(∂ut) - Δu - ϵΔ∂ut = g with u(0, ⋅) = u0 where f is a non-monotone Lipschitz-continuous function, ϵ > 0 and [Formula: see text]. We show the existence of a critical value ϵ0 >0 such that: if ϵ > ϵ0, then the problem admits a unique solution; if ϵ = ϵ0, the solution is unique and it exists under an additional assumption on f; if ϵ < ϵ0, then the solution is not unique in general. Passing to the limit with ϵ to 0+, we prove the existence (and uniqueness) of the solution of the Barenblatt differential inclusion Δu + g ∈ f(∂ut) for a class of maximal monotone operators f. Next, we give an extension of the main result for a stochastic perturbation of the problem and we give some numerical illustrations of the Barenblatt and the Barenblatt–Sobolev equation.



2008 ◽  
Vol 44 (1) ◽  
pp. 115-123 ◽  
Author(s):  
M. V. Korovina
Keyword(s):  


2007 ◽  
Vol 44 (2) ◽  
pp. 185-203 ◽  
Author(s):  
G. M. Amiraliyev ◽  
Hakki Duru ◽  
I. G. Amiraliyeva


2007 ◽  
Vol 43 (4) ◽  
pp. 525-535 ◽  
Author(s):  
M. V. Korovina


2007 ◽  
Vol 43 (3) ◽  
pp. 381-395 ◽  
Author(s):  
M. V. Korovina


1999 ◽  
Vol 51 (9) ◽  
pp. 1330-1342
Author(s):  
V. N. Los' ◽  
Ya. A. Roitberg


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