Weak-strong uniqueness for a class of degenerate parabolic cross-diffusion systems
نویسندگان
چکیده
Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown coincide with the unique strong solution determined by same initial condition on maximal existence interval latter. The proof relies an estimate established for relative entropy associated system.
منابع مشابه
Existence and uniqueness of weak solutions for a class of nonlinear divergence type diffusion equations
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کاملA Note on the Uniqueness of Weak Solutions to a Class of Cross-diffusion Systems
Abstract. The uniqueness of bounded weak solutions to strongly coupled parabolic equations in a bounded domain with no-flux boundary conditions is shown. The equations include cross-diffusion and drift terms and are coupled selfconsistently to the Poisson equation. The model class contains special cases of the Maxwell-Stefan equations for gas mixtures, generalized Shigesada-Kawasaki-Teramoto eq...
متن کاملUniqueness of Piecewise Smooth Weak Solutions of Multidimensional Degenerate Parabolic Equations1
We study the degenerate parabolic equation ut +∇ · f = ∇ · (Q∇u) + g, where (x, t) ∈ R ×R+, the flux ~ f , the viscosity coefficient Q and the source term g depend on (x, t, u) and Q is nonnegative definite. Due to the possible degeneracy, weak solutions are considered. In general, these solutions are not uniquely determined by the initial data and, therefore, additional conditions must be impo...
متن کاملUNIQUENESS OF SOLUTION FOR A CLASS OF STEFAN PROBLEMS
This paper deals with a theoretical mathematical analysis of one-dimensional solidification problem, in which kinetic undercooling is incorporated into the This temperature condition at the interface. A model problem with nonlinear kinetic law is considered. We prove a local result intimate for the uniqueness of solution of the corresponding free boundary problem.
متن کاملThe Regularity of General Parabolic Systems with Degenerate Diffusion
The aim of the talk is twofold. On one hand we want to present a new technique called p-caloric approximation, which is a proper generalization of the classical compactness methods first developed by DeGiorgi with his Harmonic Approximation Lemma. This last result, initially introduced in the setting of Geometric Measure Theory to prove the regularity of minimal surfaces, is nowadays a classica...
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: Archivum mathematicum
سال: 2023
ISSN: ['0044-8753', '1212-5059']
DOI: https://doi.org/10.5817/am2023-2-201