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A quasilinear degenerate parabolic equation

A quasilinear degenerate parabolic equation
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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 \(\phi\leq u\leq \psi\).
Lucio Boccardo, François Murat, Jean-Pierre Puel   +2 more
exaly   +4 more sources

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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On the Blow-up for Quasilinear Parabolic Equations

Journal of Partial Differential Equations, 1993
Summary: This article is concerned with the position of blow-up points, blow up rate and an isoperimetric problem for the equation \(u_ t = \Delta u^ m + u^ p\) \((p>m \geq 1)\) in a convex bounded domain.
Wang, Liwen, Chen, Qingyi
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Insensitizing controls for a class of quasilinear parabolic equations

Journal of Differential Equations, 2012
This paper is addressed to showing the existence of insensitizing controls for a class of quasilinear parabolic equations with homogeneous Dirichlet boundary conditions.
Liu, Xu
exaly   +2 more sources

Maximal regularity in continuous interpolation spaces and quasilinear parabolic equations

Journal of Evolution Equations, 2001
In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions.
Philippe Clement, Gieri Simonett, Simonett Gieri   +2 more
exaly   +1 more source

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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fisher, Brian, Liu, Z.
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On Systems of Singular Quasilinear Parabolic Equations and Inequalities

Journal of Mathematical Sciences, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mitidieri, E., Pokhozhaev, S. I.
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