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A quasilinear degenerate parabolic equation

A quasilinear degenerate parabolic equation
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Central manifolds of quasilinear parabolic equations

Ukrainian Mathematical Journal, 1998
This paper deals with a nonlinear parabolic problem of the following form \[ \frac{\partial u}{\partial t}- \sum_{|\alpha |= 2m} a_{\alpha}(x,u,\dots, D^{\beta}u) D^{\alpha } u= f (x, u,\dots, D^{\beta}u), \quad |\beta |\leq 2m-1, \tag{1} \] where \( \alpha =(\alpha_{1},\dots, \alpha_{n}) \) is a multi-index and \( D^{\alpha } = \partial^{|\alpha |} / \
Belan, E. P., Lykova, O. B.
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Generalized Quasilinearization for Quasilinear Parabolic Equations with Nonlinearities of DC Type

Journal of Optimization Theory and Applications, 2001
The authors consider an initial-boundary value problem for a class of quasilinear parabolic equations whose lower-order nonlinearity is of d.c. function type (difference of two convex functions) with respect to the dependent variable. Combining the method of quasilinearization with the well-known method of upper and lower solutions together with the ...
Carl, S., Lakshmikantham, V.
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Removable Singularities and Quasilinear Parabolic Equations

Proceedings of the London Mathematical Society, 1984
On etablit un theoreme sur les singularites eliminables pour des equations parabiliques ...
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On the Solvability of Double Degenerate Quasilinear Parabolic Equations

Acta Mathematica Hungarica, 2002
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Fisher, Brian, Liu, Z.
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On Systems of Singular Quasilinear Parabolic Equations and Inequalities

Journal of Mathematical Sciences, 2003
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Mitidieri, E., Pokhozhaev, S. I.
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Some quasilinear parabolic equations

Nonlinear Analysis: Theory, Methods & Applications, 1991
The author is concerned with finding \(u\in L^ q(0,T,W_ 0^{1,q}(\Omega))\) satisfying an equation of the form \(A(t)u+F(u,Du)=S\) with \(S\) and \(u(0)\) given and \(A(t)\) a quasilinear parabolic operator. The author remarks that in two cases results concerning existence have already been obtained, specifically when \(S\in L^{p'}(0,T,W^{- 1,p'}(\Omega)
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A Strongly Degenerate Quasilinear Equation: the Parabolic Case

Archive for Rational Mechanics and Analysis, 2005
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Andreu, Fuensanta, Caselles, Vicent, Mazón, José M.   +2 more
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Existence results for some quasilinear parabolic equations

Nonlinear Analysis: Theory, Methods & Applications, 1989
A quasilinear parabolic equation is considered. Minimal regularity of the data and a natural growth condition are assumed. It is shown that if there exist a subsolution \(\phi\) and a supersolution \(\psi\) such that \(\phi\leq \psi\), then there exists at least one weak solution u such that \(\phi\leq u\leq \psi\).
BOCCARDO, Lucio, François Murat, Jean Pierre Puel   +2 more
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Quasilinear Parabolic Equations in Lp

2006
The paper contains a local existence and uniqueness result for quasilinear parabolic equations on a three-dimensional domain including mixed boundary conditions and discontinuous coefficients.
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