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Convergence for Degenerate Parabolic Equations

Journal of Differential Equations, 1999
The authors consider degenerate parabolic problems of the form \[ \begin{aligned} u_t-\varphi \bigl(u(x,t) \bigr)_{xx}= f\bigl(u(x,t) \bigr),\quad & x\in (-L,L),\;t>0,\\ u(-L,t)= u(L,t)=0, \quad & t>0,\\ u(x,0)= u_0(t)\geq 0,\quad & x\in (-L,L), \end{aligned} \] where \(\varphi\) and \(f\) are sufficiently regular functions satisfying \(\varphi(0)=0\),
Eduard Feireisl
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A System of Degenerate Parabolic Equations

SIAM Journal on Mathematical Analysis, 1990
The system of two nonlinear equations which arises in plasma physics is considered. The equations are of degenerate parabolic type. The global existence theorem for the Cauchy problem is proved. The proof is based on the Lagrangian transformation, thus using a particular structure of the system.
BERTSCH, MICHIEL, Kamin, S.
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A numerical approach to degenerate parabolic equations

Numerische Mathematik, 2002
A class of degenerate parabolic equations typically describing the gas flow through porous media is considered. The numerical difficulties in treating such problems arise from the nonlinear degeneracy of the equations. Such problems can be investigated through a parabolic regularization which can be constructed in different ways.
Iuliu Sorin Pop, Wen-An Yong
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Nonlinear Degenerate Parabolic Equations

Acta Mathematica Hungarica, 1997
The author proves the existence of weak solutions of the nonlinear degenerate parabolic initial-boundary value problem \[ {{\partial u}\over{\partial t}} - \sum_{i=1}^N D_iA_i(x,t,u,Du) + A_0(x,t,u,Du) = f(x,t)\quad\text{ in }\Omega\times(0,T), \] \[ u(x,0) = u_0(x)\quad \hbox{ in }\Omega, \] in the space \(L^p(0,T,W^{1,p}_0(v,\Omega))\), where ...
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Dynamics for a stochastic degenerate parabolic equation

Computers & Mathematics with Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingquan Chang, Dandan Li, Chunyou Sun
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Homogenization of degenerate elliptic‐parabolic equations

Asymptotic Analysis, 2004
In this paper we give a result of G‐convergence for a class of strongly degenerate parabolic equations in the case of periodic coefficients. The operators have the form μ(x)∂ t −div(a(x,t)·D) where the quadratic form associated to a(x,t) is degenerating as a Muckenhoupt weight and the ...
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Degenerate integrodifferential equations of parabolic type

2006
Il contributo è un articolo scientifico originale, non pubblicato altrove in nessuna forma, e sottoposto a referee. Il volume contiene solo articoli originali.
FAVINI, ANGELO, A. LORENZI, H. TANABE
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Quenching for degenerate parabolic equations

Nonlinear Analysis: Theory, Methods & Applications, 1998
The authors study local and global existence of nonnegative solutions of the equation \(u_t-(p(x)u_x)_x=f(u)\), \(x\in(0,a)\), \(t>0\), complemented by homogeneous Dirichlet boundary conditions and the initial condition \(u(x,0)=u_0(x)\). Here \(p,f,u_0\) satisfy certain regularity properties and \(p(0)=0\), \(p(x)>0\) for \(x>0\), \(\int_0^A dx/p(x)
Ke, L., Ning, S.
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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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Hyperbolic Phenomena in a Degenerate Parabolic Equation

Journal of Partial Differential Equations, 1997
M. Bertsch and R. Dal Passo [1] considered the equation u_t =  (φ(u)ψ(u_z))x., where φ > 0 and ψ is a strictly increasing function with lim_{s → ∞} ψ(s) = ψ_∞ 0 is essential in their paper. In the present paper, we study the above equation under the degenerate condition φ(0) = 0.
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