Existence and regularity results for parabolic equations with degenerate coercivity

2017 ◽  
Vol 63 (5) ◽  
pp. 715-729
Author(s):  
Y. El Hadfi ◽  
A. Benkirane ◽  
A. Youssfi

2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah

Abstract In this paper we prove some existence and regularity results for nonlinear unilateral problems with degenerate coercivity via the penalty method.





2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tran Ngoc Thach ◽  
Devendra Kumar ◽  
Nguyen Hoang Luc ◽  
Nguyen Huy Tuan

<p style='text-indent:20px;'>Solutions of a direct problem for a stochastic pseudo-parabolic equation with fractional Caputo derivative are investigated, in which the non-linear space-time-noise is assumed to satisfy distinct Lipshitz conditions including globally and locally assumptions. The main aim of this work is to establish some existence, uniqueness, regularity, and continuity results for mild solutions.</p>



2018 ◽  
Vol 24 (2) ◽  
pp. 859-872 ◽  
Author(s):  
Hayk Mikayelyan

An optimal rearrangement problem in a cylindrical domainΩ=D× (0, 1) is considered, under the constraint that the force function does not depend on thexnvariable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain     Δu(x′,xn) =χ{v>0}(x′) +χ{v=0}(x′) [∂νu(x′,0) +∂νu(x′, 1)]arising from minimization of the functional     ∫Ω½;|∇u(x)|2+χ{v>0}(x′)u(x) dx,wherev(x′) =∫01u(x′,t)dt, and∂νuis the exterior normal derivative ofuat the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.



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