منابع مشابه
Stability of Solutions of Quasilinear Parabolic Equations
Abstract. We bound the difference between solutions u and v of ut = a∆u+ divx f + h and vt = b∆v + divx g + k with initial data φ and ψ, respectively, by ‖u(t, ·)− v(t, ·)‖Lp(E) ≤ AE(t)‖φ−ψ‖ 2ρp L∞(Rn) +B(t)(‖a− b‖∞ + ‖∇x · f − ∇x · g‖∞ + ‖fu − gu‖∞ + ‖h− k‖∞)p |E| ηp . Here all functions a, f , and h are smooth and bounded, and may depend on u, x ∈ R, and t. The functions a and h may in additi...
متن کاملBackward selfsimilar solutions of supercritical parabolic equations
We consider the exponential reaction–diffusion equation in space-dimension n ∈ (2, 10). We show that for any integer k ≥ 2 there is a backward selfsimilar solution which crosses the singular steady state k-times. The sameholds for the power nonlinearity if the exponent is supercritical in the Sobolev sense and subcritical in the Joseph–Lundgren sense. © 2008 Elsevier Ltd. All rights reserved.
متن کاملAveraging for Fundamental Solutions of Parabolic Equations
Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order, "-dependent parabolic partial di erential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the fundamental solution of an \averaged" parabolic equation, we bring forth a novel approach to compar...
متن کاملBoundary Behavior of Solutions of Parabolic Equations
A boundary backward Harnack inequality is proved for positive solutions of second order parabolic equations in non-divergence form in a bounded cylinder Q = (0; T) which vanish on @ x Q = @ (0; T) ; where is a bounded Lipschitz domain in R n. This inequality is applied to the proof of the HH older continuity of the quotient of two positive solutions vanishing on a portion of @ x Q: 1. Introduct...
متن کاملPreservation of Convexity of Solutions to Parabolic Equations
In the present paper we find necessary and sufficient conditions on the coefficients of a parabolic equation for convexity to be preserved. A parabolic equation is said to preserve convexity if given a convex initial condition, any solution of moderate growth remains a convex function of the spatial variables for each fixed time.
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: Notices of the American Mathematical Society
سال: 2016
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1312