Self-similar blow-up for a reaction-diffusion system
نویسندگان
چکیده
منابع مشابه
Self-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 کاملBlow-up for a reaction-diffusion equation with variable coefficient
We study the blow-up behavior for positive solutions of a reaction–diffusion equationwith nonnegative variable coefficient. When there is no stationary solution, we show that the solution blows up in finite time. Under certain conditions, we then show that any point with zero source cannot be a blow-up point. © 2012 Elsevier Ltd. All rights reserved.
متن کاملOn Self-similar Blow-up in Evolution Equations of Monge–ampère Type: a View from Reaction-diffusion Theory
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 (0.1) ut = −|Du|+ |u|u in R × R+, where in two-dimensions |D2u| = uxxuyy − (uxy) and p > 1 is a fixed exponent. For a class of “dominated concave” and compactly supported radial initial data u0(x) ≥ 0, th...
متن کاملSelf-Similar Blow-Up in Higher-Order Semilinear Parabolic Equations
We study the Cauchy problem in R × R+ for one-dimensional 2mth-order, m > 1, semilinear parabolic PDEs of the form (Dx = ∂/∂x) ut = (−1) D x u + |u| u, where p > 1, and ut = (−1) D x u + e u with bounded initial data u0(x). Specifically, we are interested in those solutions that blow up at the origin in a finite time T . We show that, in contrast to the solutions of the classical secondorder pa...
متن کاملStable Ground States and Self-Similar Blow-Up Solutions for the Gravitational Vlasov-Manev System
In this work, we study the orbital stability of steady states and the existence of blow-up self-similar solutions to the so-called Vlasov-Manev (VM) system. This system is a kinetic model which has a similar Vlasov structure as the classical Vlasov-Poisson system, but is coupled to a potential in −1/r−1/r (Manev potential) instead of the usual gravitational potential in −1/r, and in particular ...
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: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00104-6