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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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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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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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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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On the convergence of a class of degenerate parabolic equations
Journal de Mathématiques Pures et Appliquées, 1998 The authors study the convergence of the Cauchy-Dirichlet problems for a sequence of parabolic operators in the divergence form \(P_h =\frac{\partial}{\partial t} - \text{div} (a_h(x,t) D)\), as \(h\to\infty\), where \(a_h(x,t) =[a_{h,ij}(x,t)]_{i,j =1,\dots n}\) are matrices of measurable functions defined on a bounded open cylinder \(\Omega\times (0 ...
PARONETTO, FABIO, F. Serra Cassano
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A degenerate parabolic equation in noncylindrical domains
Mathematische Annalen, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
BERTSCH, MICHIEL +2 more
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Difference schemes for degenerate parabolic equations [PDF]
Mathematics of Computation, 1986 Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate L 1 {L^1} -space, and the rate of convergence to the semigroup solution in L 1
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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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Null controllability of degenerate parabolic operators with drift
Networks and Heterogeneous Media, 2007 We give null controllability results for some degenerate parabolic equations in non divergence form with a drift term in one space dimension. In particular, the coefficient of the second order term may degenerate at the extreme points of the space domain.
Piermarco Cannarsa +2 more
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Asymptotic expansions for degenerate parabolic equations
Comptes Rendus. Mathématique, 2014 Abstract We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short ...
PASCUCCI, ANDREA +2 more
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