Results 251 to 260 of about 43,069 (282)

A nonlinear degenerate parabolic equation

Nonlinear Analysis: Theory, Methods & Applications, 1990
The 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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A Degenerate Parabolic Logistic Equation

2014
We 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, Rosa Pardo, Aníbal Rodríguez-Bernal   +2 more
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ON UNIQUENESS CLASSES FOR DEGENERATING PARABOLIC EQUATIONS

Mathematics of the USSR-Sbornik, 1971
We 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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Cauchy’s Problem for Degenerate Quasilinear Parabolic Equations

Theory of Probability & Its Applications, 1964
In this paper we consider the differential properties of the solution to the Cauchy problem for the quasilinear parabolic equation \[ (1)\qquad \frac{{\partial v}}{{\partial t}} = \frac{1}{2}\sum\limits_{i,j = 1}^n {c_{ij} } (t,x,v)\frac{{\partial ^2 v}}{{\partial x_i \partial x_i }} + \sum\limits_{i = 1}^n {a_i } (t,x,v)\frac{{\partial v}}{{\partial ...
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Problems without Initial Conditions for Degenerating Parabolic Equations

Differential Equations, 1993
This article deals with problems for parabolic equations of the type \(a^ 2 u_ t = u_{xx} + cu_ x\) with boundary data \(u(0,t) = A \cos \omega t\). The main result is an existence and uniqueness theorem in the following cases: a) \(k=1\), \(c>1\), b ...
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Harnack's Inequality for Degenerate Parabolic Equations

Communications in Partial Differential Equations, 1991
(1991). Harnack's Inequality for Degenerate Parabolic Equations. Communications in Partial Differential Equations: Vol. 16, No. 4-5, pp. 745-770.
Cristian E. Gutiérrez, Richard L. Wheeden   +1 more
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Critical exponents of degenerate parabolic equations

1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Degenerate Parabolic and Elliptic Equations

1994
The 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 Fredholm Transformation for the Rapid Stabilization of a Degenerate Parabolic Equation

SIAM Journal on Control and Optimization, 2021
Ludovick Gagnon, Swann Marx
exaly  

Identifying unknown source in degenerate parabolic equation from final observation

Inverse Problems in Science and Engineering, 2021
Zhiyuan Li
exaly