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
Keyword(s):  
Parabolic Equations ◽  
Degenerate Coercivity ◽  
Existence And Regularity Results ◽  
Regularity Results

Existence and regularity results for unilateral problems with degenerate coercivity

2019 ◽  
Vol 69 (6) ◽  
pp. 1351-1366 ◽  
Author(s):  
Hocine Ayadi ◽  
Rezak Souilah
Keyword(s):  
Penalty Method ◽  
Degenerate Coercivity ◽  
Unilateral Problems ◽  
Existence And Regularity Results ◽  
Regularity Results

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

scholarly journals Some existence and regularity results for abstract non-autonomous parabolic equations

1984 ◽  
Vol 99 (1) ◽  
pp. 9-64 ◽  
Author(s):  
Paolo Acquistapace ◽  
Brunello Terreni
Keyword(s):  
Parabolic Equations ◽  
Existence And Regularity Results ◽  
Regularity Results

scholarly journals Existence and regularity results for stochastic fractional pseudo-parabolic equations driven by white noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Tran Ngoc Thach ◽  
Devendra Kumar ◽  
Nguyen Hoang Luc ◽  
Nguyen Huy Tuan
Keyword(s):  
Parabolic Equation ◽  
White Noise ◽  
Linear Space ◽  
Parabolic Equations ◽  
Caputo Derivative ◽  
Direct Problem ◽  
Mild Solutions ◽  
Fractional Caputo Derivative ◽  
Existence And Regularity Results ◽  
Regularity Results

<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>

Cylindrical optimal rearrangement problem leading to a new type obstacle problem

2018 ◽  
Vol 24 (2) ◽  
pp. 859-872 ◽  
Author(s):  
Hayk Mikayelyan
Keyword(s):  
Comparison Principle ◽  
Obstacle Problem ◽  
Normal Derivative ◽  
Force Function ◽  
Cylindrical Domain ◽  
New Type ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Cylindrical Axis

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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