Positive solutions of the heat equation
نویسندگان
چکیده
منابع مشابه
Classification of positive solutions of heat equation with supercritical absorption
Let q ≥ 1 + 2 N . We prove that any positive solution of (E) ∂tu − ∆u + u = 0 in R × (0,∞) admits an initial trace which is a nonnegative Borel measure, outer regular with respect to the fine topology associated to the Bessel capacity C 2 q ,q in R N (q = q/q − 1)) and absolutely continuous with respect to this capacity. If ν is a nonnegative Borel measure in R with the above properties we cons...
متن کاملWhen Does a Schrödinger Heat Equation Permit Positive Solutions
We introduce some new classes of time dependent functions whose defining properties take into account of oscillations around singularities. We study properties of solutions to the heat equation with coefficients in these classes which are much more singular than those allowed under the current theory. In the case of L potentials and L 2 solutions, we give a characterization of potentials which ...
متن کاملUnbounded solutions of the nonlocal heat equation
We consider the Cauchy problem posed in the whole space for the following nonlocal heat equation: ut = J ∗u−u , where J is a symmetric continuous probability density. Depending on the tail of J , we give a rather complete picture of the problem in optimal classes of data by: (i) estimating the initial trace of (possibly unbounded) solutions; (ii) showing existence and uniqueness results in a su...
متن کاملOn the Positive Solutions of Matukuma Equation
3/(1 + r2) for (1.2) with p = 3 which confirms part of his conjecture. Since then there seems to be very little mathematical contribution in the literature on this equation until the recent works of W.-M. Ni and S. Yotsutani [NY1,2], Y. Li and W.-M. Ni [LN2], and E.S. Noussair and C.A. Swanson [NS]. First, it was observed in [NY2] and [LN2] that Eddington’s model does not have any positive enti...
متن کاملThe Persistence of Log-concavity for Positive Solutions of the One Dimensional Heat Equation
Consider positive solutions of the one-dimensional heat equation. The space variable x lies in (?a; a): the time variable t in (0; 1). When the solution u satisses (i) u(a; t) = 0, and (ii) u(:; 0) is logconcave, we give a new proof based on the Maximum Principle, that, for any xed t > 0, u(:; t) remains logconcave. The same proof techniques are used to establish several new results related to ...
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: Bulletin of the American Mathematical Society
سال: 1963
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1963-10882-4