منابع مشابه
Runge - Kutta Approximation of Quasi - Linear Parabolic Equations
We study the convergence properties of implicit Runge-Kutta methods applied to time discretization of parabolic equations with timeor solutiondependent operator. Error bounds are derived in the energy norm. The convergence analysis uses two different approaches. The first, technically simpler approach relies on energy estimates and requires algebraic stability of the RungeKutta method. The seco...
متن کاملRenormalized Entropy Solutions for Quasi-linear Anisotropic Degenerate Parabolic Equations
We prove the well-posedness (existence and uniqueness) of renormalized entropy solutions to the Cauchy problem for quasi-linear anisotropic degenerate parabolic equations with L1 data. This paper complements the work by Chen and Perthame [9], who developed a pure L1 theory based on the notion of kinetic solutions.
متن کاملGradient estimates for degenerate quasi-linear parabolic equations
For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients infinitesimally form bounded with respect to the Laplacian we obtain Lq-estimates for the gradients of solutions, and for the lower order coefficients from a Kato-type class we show that the solutions are Lipschitz continuous with respect to the space var...
متن کاملA Quasi-linear Parabolic System of Chemotaxis
We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n-dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A(u), and that the diffusion coefficient of v is a positive constant. If A(u) is a positive constant, the system is referred to as socalled Keller-Segel system. In the case where th...
متن کاملOn quasi-linear stochastic partial differential equations
We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1967
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000012459