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ON UNIQUENESS CLASSES FOR DEGENERATING PARABOLIC EQUATIONS
Mathematics of the USSR-Sbornik, 1971We study the uniqueness classes of a generalized solution of the Cauchy problem (1)when the matrix is degenerate. A generalized solution is introduced with the help of an infinitesimal operator of a Markov process connected with the operator in (1).
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Symmetry for degenerate parabolic equations
Archive for Rational Mechanics and Analysis, 1989For ...
ALESSANDRINI, GIOVANNI, GAROFALO N.
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Some degenerate nonlinear parabolic equations
九州大学教養部数学雑誌, 1984The author proves existence, uniqueness and asymptotic behaviour of solutions of the initial value problem for the generalized porous medium equation on a bounded domain in \({\mathbb{R}}^ n\). In various cases, decay notes, positivity and uniqueness are given which extend known results in various directions.
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Degenerate and Singular Parabolic Equations
2011Let E be an open set in \(\mathbb{R}^{N}\) and for T > 0 let E T denote the cylindrical domain E × (0, T].
Emmanuele DiBenedetto +2 more
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On Degenerate Nonlinear Parabolic Equations on the Bohr Compactum
Differential Equations, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Degenerate Parabolic Logistic Equation
2014We analyze the behavior of positive solutions of parabolic equations with a class of degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels.
José M. Arrieta +2 more
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On the homogenization of degenerate parabolic equations
Acta Mathematicae Applicatae Sinica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Critical exponents of degenerate parabolic equations
1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Degenerate Parabolic and Elliptic Equations
1994The region where the equation deteriorates is fixed for linear and semilinear degenerate equations. The cases usually discussed are that the degenerate region is on the boundary. The two approaches are often used. One is the barrier argument and another is introducing the weighted Sobolev spaces.
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A nonlinear degenerate parabolic equation
Nonlinear Analysis: Theory, Methods & Applications, 1990The Cauchy problem for the equation \(u_ t-\alpha (u)_{xx}+\beta (u)_ x\ni f\) has a unique integral solution in \(L^ 1({\mathbb{R}})\) when \(\alpha\) and \(\beta\) are maximal monotone graphs in \({\mathbb{R}}\times {\mathbb{R}}\), \(0\in Int D(\alpha)\), \(\beta\) is dominated by \(\alpha\) in a certain sense, and at each point of their common ...
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