Results 241 to 250 of about 40,292 (276)

Blow-up behavior of solutions to a degenerate parabolic–parabolic Keller–Segel system

Mathematische Annalen, 2016
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Ishige, Kazuhiro, Laurencot, Philippe, Mizoguchi, Noriko   +2 more
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Degenerate parabolic equation and unilateral constraint systems

Applied Mathematics and Mechanics, 1996
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Degenerate and singular parabolic systems

1993
We turn now to quasilinear systems whose principal part becomes either degenerate or singular at points where. To present a streamlined cross section of the theory, we refer to the model system $$ \left\{{\begin{array}{*{20}{c}} {u \equiv \left( {{u_1},{u_2}, \ldots,{u_m}} \right),m\in N,}\\ {{u_i}\in{C_{loc}}\left({0,T;L_{loc}^2\left(\Omega\right)}
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Some Estimates of a System of Degenerate Parabolic Equations

Journal of Dynamical and Control Systems, 2013
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A degenerate parabolic system with nonlocal boundary condition

Applicable Analysis, 2011
In this article, we investigate the blow-up properties of the positive solutions to a degenerate parabolic system with nonlocal boundary condition. We give the criteria for finite time blow-up or global existence, which shows the important influence of nonlocal boundary.
Yongsheng Mi, Chunlai Mu, Botao Chen
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Hölder estimates for second-order quasilinear degenerate parabolic systems

Journal of Soviet Mathematics, 1990
See the review in Zbl 0669.35056.
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The cauchy problem for a quasilinear degenerate parabolic system

Nonlinear Analysis: Theory, Methods & Applications, 1994
The paper is concerned with the Cauchy problem \(U_ t = \Delta (| U |^{m - 1} U)\), \(U(x,0) = U_ 0(x)\), \(x \in \mathbb{R}^ N\), \(t \in (0,T)\), \(U = (u_ 1, \dots, u_ n)\), \(| U |^ 2 = u^ 2_ 1 + \cdots + u^ 2_ n\), \(m>1\). This parabolic system arises in many applications (a typical example is the porous medium equation with \(n=1)\).
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Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression

SIAM Journal on Applied Mathematics, 2003
Mathematical models for the controlled sedimentation of polydisperse suspensions of small particles, which belong to a finite number of special differing in size or density are suspended in viscous fluid, are important in many theoretical and practical applications.
Berres, Stefan, Bürger, Raimund, Karlsen, Kenneth H., Tory, Elmer M.   +3 more
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Regularity for degenerate elliptic and parabolic systems

2013
In this work local behavior for solutions to the inhomogeneous p-Laplace in divergence form and its parabolic version are studied. It is parabolic and non-linear generalization of the Calderon-Zygmund theory for the Laplace operator. I.e. the borderline case BMO is studied.
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Finite-time blow-up for quasilinear degenerate Keller–Segel systems of parabolic–parabolic type

Journal of Differential Equations, 2018
The authors study energy solutions to the quasilinear degenerate chemotaxis system \[ \begin{cases} u_t = \Delta u^m - \nabla \cdot (u^{q-1} \nabla v), \quad & (x,t) \in \Omega \times (0,\infty), \\ v_t = \Delta v -v +u, \quad & (x,t) \in \Omega \times (0,\infty), \end{cases} \] endowed with homogeneous Neumann boundary conditions and nonnegative ...
Hashira, Takahiro, Ishida, Sachiko, Yokota, Tomomi   +2 more
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