Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
نویسندگان
چکیده
We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.
منابع مشابه
Blowup Analysis for a Nonlocal Reaction Diffusion Equation with Potential
In this paper we investigate a nonlocal reaction diffusion equation with potential, under Neumann boundary. We obtain the complete classification of the parameters for which the solution blows up in finite time or exists globally. Moreover, we study the blowup rate and the blowup set for the blowup solution. Key–Words: Nonlocal diffusion, Blow up, Blowup rate, Blowup set
متن کاملA Blowup Problem of Reaction Diffusion Equation Related to the Diffusion Induced Blowup Phenomenon
This work studies nonnegative solutions for the Cauchy, Neumann, and Dirichlet problems of the logistic type equation ut = ∆u+ μu p − a(x)u with p, q > 1, μ > 0. The finite time blowup results for nonnegative solutions under various restrictions on a(x), p, q, μ are presented. Applying the results allows one to construct some reaction diffusion systems with
متن کاملOn a Nonlocal Aggregation Model with Nonlinear Diffusion
We consider a nonlocal aggregation equation with nonlinear diffusion which arises from the study of biological aggregation dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution develops L∞ x -norm blowup in finite time.
متن کاملPulses and waves for a bistable nonlocal reaction-diffusion equation
A bistable nonlocal reaction-diffusion equation is studied. Solutions in the form of simple and periodic travelling waves, single and multiple pulses are observed in numerical simulations. Successive transitions from simple waves to periodic waves and to stable pulses are described.
متن کاملDynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection.
A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Mathematics
دوره 2012 شماره
صفحات -
تاریخ انتشار 2012