On uniqueness for a rough transport–diffusion equation
نویسندگان
چکیده
منابع مشابه
Uniqueness of solutions for a mean field equation on torus
We consider on a two-dimensional flat torus T the following equation ∆u + ρ ( eu ∫ T e u − 1 |T | ) = 0. When the fundamental domain of the torus is (0, a) × (0, b) (a ≥ b), we establish that the constants are the unique solutions whenever ρ ≤ { 8π if b a ≥ π4 , 32 b a if b a ≤ π4 , and this result is sharp if b a ≥ π4 . A similar conclusion is obtained for general two-dimensional torus by cons...
متن کاملOn existence and uniqueness of solutions of a nonlinear Volterra-Fredholm integral equation
In this paper we investigate the existence and uniqueness for Volterra-Fredholm type integral equations and extension of this type of integral equations. The result is obtained by using the coupled fixed point theorems in the framework of Banach space $ X=C([a,b],mathbb{R})$. Finally, we give an example to illustrate the applications of our results.
متن کاملA Uniqueness Result for Scattering by Infinite Rough Surfaces
Consider the Dirichlet boundary value problem for the Helmholtz equation in a nonlocally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the...
متن کاملOn uniqueness and decay of solution for Hirota equation
We address the question of the uniqueness of solution to the initial value problem associated to the equation ∂tu+ iα∂ 2 xu+ β∂ 3 xu+ iγ|u| 2 u+ δ|u|∂xu+ ǫu 2 ∂xu = 0, x, t ∈ R, and prove that a certain decay property of the difference u1 − u2 of two solutions u1 and u2 at two different instants of times t = 0 and t = 1, is sufficient to ensure that u1 = u2 for all the time.
متن کاملBackward uniqueness for the heat equation
According to Gurarii and Matsaev [5], these properties are equivalent, but no proof was ever published. Here is a summary of known results. When n = 1, both properties hold if and only if D is a bounded interval. For PII this is evident, for PI this follows from the results of Tychonov [7]. When n = 2, and D is an angular sector {z : | arg z| < α}, the property PII holds if and only if α < 45◦....
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: Comptes Rendus Mathematique
سال: 2016
ISSN: 1631-073X
DOI: 10.1016/j.crma.2016.05.003