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Degenerate singular parabolic problems with natural growth [PDF]
Opuscula MathematicaIn this paper, we study the existence and regularity results for nonlinear singular parabolic problems with a natural growth gradient term \[\begin{cases}\frac{\partial u}{\partial t}-\operatorname{div}((a(x,t)+u^{q})|\nabla u|^{p-2}\nabla u)+d(x,t)\frac{
Mounim El Ouardy +2 more
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Expansion of positivity to a class of doubly nonlinear parabolic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We establish the expansion of positivity of the nonnegative, local, weak solutions to the class of doubly nonlinear parabolic equations $$\partial_t (u^{q}) -\operatorname{div}{(|D u|^{p-2} D u)}=0, \qquad\ p>1 \ \text{and} \ q>0$$ considering ...
Eurica Henriques
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The cost of controlling strongly degenerate parabolic equations [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2020 We consider the typical one-dimensional strongly degenerate parabolic operator Pu = ut − (xαux)x with 0 < x < ℓ and α ∈ (0, 2), controlled either by a boundary control acting at x = ℓ, or by a locally distributed control. Our main goal is to study the dependence of the so-called controllability cost needed to drive an initial condition to rest ...
Cannarsa, P. +2 more
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On the Weak Characteristic Function Method for a Degenerate Parabolic Equation
Journal of Function Spaces, 2019 For a nonlinear degenerate parabolic equation, how to impose a suitable boundary value condition to ensure the well-posedness of weak solutions is a very important problem.
Huashui Zhan
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Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces
Mathematics in Engineering, 2023 We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of $ p $-Laplacian type with $ p > \frac{2n}{n+2} $ in weighted Lebesgue spaces $ L^q_w $.
Mikyoung Lee, Jihoon Ok
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On the convergence of a class of degenerate parabolic equations
Journal de Mathématiques Pures et Appliquées, 1998 Abstract In this paper we study the convergence of the Cauchy-Dirichlet problems for a sequence of parabolic operators P h = ∂ ∂t − div (a h (x,t) · D) , where the matrices of the coefficient ah(x,t) verify the following degenerate elliptic condition: λ h (x)|ζ| 2 ≤ (a h (x,t)⋯ζ,ζ)≤Lλ h (x)|ζ|
PARONETTO, FABIO, F. Serra Cassano
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Optimal Control Problems of a Class of Nonlinear Degenerate Parabolic Equations
MathematicsThe optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic ...
Yang Na +3 more
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Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions
Abstract and Applied Analysis, 2006 We consider a class of singularly perturbed parabolic equations for which the degenerate equations obtained by setting the small parameter equal to zero are algebraic equations that have several roots.
Adelaida B. Vasil'eva +1 more
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Dissipation enhancement for a degenerated parabolic equation
Communications in Mathematical Sciences, 2023 22 ...
Feng, Yu, Hu, Bingyang, Xu, Xiaoqian
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A strongly degenerate parabolic aggregation equation [PDF]
Communications in Mathematical Sciences, 2011 This paper is concerned with a strongly degenerate convection-diffusion equation in one space dimension whose convective flux involves a non-linear function of the total mass to one side of the given position. This equation can be understood as a model of aggregation of the individuals of a population with the solution representing their local density.
Betancourt, F. +2 more
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