Anomalous exponents of self-similar blow-up solutions to an aggregation equation in odd dimensions
نویسندگان
چکیده
We calculate the scaling behavior of the second-kind self-similar blow-up solution of an aggregation equation in odd dimensions. This solution describes the radially symmetric finite-time blowup phenomena and has been observed in numerical simulations of the dynamic problem. The nonlocal equation for the self-similar profile is transformed into a system of ODEs that is solved using a shooting method. The anomalous exponents are then retrieved from this transformed system.
منابع مشابه
Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملSelf-similar blow-up for a diffusion–attraction problem
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see, e.g., Brenner M P et al 1999 Nonline...
متن کاملOn Formation of a Locally Self-similar Collapse in the Incompressible Euler Equations
The paper addresses the question of existence of a locally self-similar blow-up for the incompressible Euler equations. Several exclusion results are proved based on the L-condition for velocity or vorticity and for a range of scaling exponents. In particular, in N dimensions if in self-similar variables u ∈ L and u ∼ 1 tα/(1+α) , then the blow-up does not occur provided α > N/2 or −1 < α ≤ N/p...
متن کاملm at h . A P ] 2 3 Ju n 20 09 SELF - SIMILAR BLOW - UP IN PARABOLIC EQUATIONS OF MONGE – AMPÈRE TYPE
We use techniques from reaction-diffusion theory to study the blow-up and existence of solutions of the parabolic Monge–Ampère equation with power source, with the following basic 2D model (0.1) u t = −|D 2 u| + |u| p−1 u in R 2 × R + , where in two-dimensions |D 2 u| = u xx u yy − (u xy) 2 and p > 1 is a fixed exponent. For a class of " dominated concave " and compactly supported radial initia...
متن کاملBlow Up Analysis for Anomalous Granular Gases
We investigate in this article the long-time behaviour of the solutions to the energydependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under statistical description, that dissipates energy during collisions. We assume that the gas is “anomalous”, in the sense that energy dissipation increases when tempera...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Appl. Math. Lett.
دوره 25 شماره
صفحات -
تاریخ انتشار 2012