Uniform Boundedness and Convergence of Solutions to Cross-Diffusion Systems
نویسندگان
چکیده
منابع مشابه
About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order
In this paper, we establish sufficient conditions under which all solutions of equation of the type x(5) + f(t, x, ẋ, ẍ, ... x , x(4)) + φ(t, ẋ, ẍ, ... x ) + ψ(t, x, ẋ, ẍ) + g(t, x, ẋ) + e(t)h(x) = p(t, x, ẋ, ẍ, ... x , x(4)) are uniformly bounded and tend to zero as t → ∞. Our theorem is stated in a more general form; it extends some related results known in the literature. Also, the relevance...
متن کاملGraph-distance Convergence and Uniform Local Boundedness of Monotone Mappings
In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...
متن کاملThe boundedness-by-entropy method for cross-diffusion systems
The global-in-time existence of bounded weak solutions to a large class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure is proved. The main feature of these systems is that the diffusion matrix may be generally neither symmetric nor positive semidefinite. The key idea is to employ a transformation of variables, determined by the entropy den...
متن کاملExistence and Uniform Boundedness of Optimal Solutions of Variational Problems
Given an x0 ∈ Rn we study the infinite horizon problem of minimizing the expression ∫ T 0 f(t, x(t), x ′(t))dt as T grows to infinity where x : [0,∞) → Rn satisfies the initial condition x(0) = x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set E ⊂ Rn the C([0, T ]) norms of approximate sol...
متن کاملUniform Boundedness of Solutions for a Class of Liénard Equations
In this article, we study a class of Liénard equations x′′(t) + f(x(t))x′(t) + g1(x(t)) + g2(x(t− τ(t)) = e(t). Under some suitable conditions, we ensure that all solutions of the above Liénard equations are uniformly bounded. Our assumptions are less restrictive than those in [9]; thus we extend some previous results.
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: Journal of Differential Equations
سال: 2002
ISSN: 0022-0396
DOI: 10.1006/jdeq.2002.4169