Regularity of solutions for quasi-linear parabolic equations
نویسندگان
چکیده
منابع مشابه
Renormalized 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 کاملGlobal Low Regularity Solutions of Quasi-linear Wave Equations
In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three space dimensions. The results are based on the end-point Strichartz estimate together with the characteristic method.
متن کاملREGULARITY FOR ENTROPY SOLUTIONS OF PARABOLIC p-LAPLACIAN TYPE EQUATIONS
In this note we give some summability results for entropy solutions of the nonlinear parabolic equation ut − div ap(x,∇u) = f in ]0, T [×Ω with initial datum in L1(Ω) and assuming Dirichlet’s boundary condition, where ap(., .) is a Carathéodory function satisfying the classical Leray-Lions hypotheses, f ∈ L1(]0, T [×Ω) and Ω is a domain in RN . We find spaces of type Lr(0, T ;Mq(Ω)) containing ...
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 کاملRunge - 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 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: 1976
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000017207