Well-posedness of the linear heat equation with a second order memory term
نویسندگان
چکیده
منابع مشابه
Well-posedness of Second Order Evolution Equation on Discrete Time
We characterize the well-posedness for second order discrete evolution equations in UMD spaces by means of Fourier multipliers and R-boundedness properties of the resolvent operator which defines the equation. Applications to semilinear problems are given.
متن کاملWell-posedness for a Higher-order Benjamin-ono Equation
In this paper we prove that the initial value problem associated to the following higher-order Benjamin-Ono equation ∂tv − bH∂ xv + a∂ xv = cv∂xv − d∂x(vH∂xv + H(v∂xv)), where x, t ∈ R, v is a real-valued function, H is the Hilbert transform, a ∈ R, b, c and d are positive constants, is locally well-posed for initial data v(0) = v0 ∈ H(R), s ≥ 2 or v0 ∈ H(R) ∩ L(R; xdx), k ∈ Z+, k ≥ 2.
متن کاملSharp Global Well-posedness for a Higher Order Schrödinger Equation
Using the theory of almost conserved energies and the “I-method” developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher order Schrödinger equation is globally wellposed in Sobolev spaces of order s > 1/4. This result is sharp.
متن کاملWell-posedness and standing waves for the fourth-order non-linear Schrödinger-type equation
We consider the initial value problem for the fourth-order non-linear Schrödinger-type equation (4NLS) which describes the motion of an isolated vortex filament. In the first part of this note we review some recent results on the time local well-posedness of (4NLS) and give the alternative proof of those results. In the second part of this note we consider the stability of a standing wave solut...
متن کاملA RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION
Let U(t, ) be solution of the Dirichlet problem y''+( t-q(t))y= 0 - 1 t l y(-l)= 0 = y(x), with variabIe t on (-1, x), for fixed x, which satisfies the initial condition U(-1, )=0 , (-1, )=1. In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigen values has been investigated . Furthermore, the leading term of the asymptotic formula for ...
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: ITM Web of Conferences
سال: 2020
ISSN: 2271-2097
DOI: 10.1051/itmconf/20203403011