Quasilinear parabolic equation - Open Access .click

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
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nonlinear parabolic equations
quasilinear parabolic equations
mathematics

degenerate parabolic equations
analysis
maximum principle

qa1-939
uniqueness
existence