A Blowup Problem of Reaction Diffusion Equation Related to the Diffusion Induced Blowup Phenomenon
نویسنده
چکیده
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
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 کاملBlowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
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...
متن کاملAsymptotics of Blowup for a Convection-diffusion Equation with Conservation
This paper deals with a parabolic partial differential equation that incorporates diffusion and convection terms and that previously has been shown to have solutions that become unbounded at a single point in finite time. The results presented here describe the limiting behavior of the solution in a neighborhood of the blowup point, as well as the asymptotic growth rate as the blowup time is ap...
متن کاملGlobal Existence and Blowup for Free Boundary Problems of Coupled Reaction-diffusion Systems
This article concerns a free boundary problem for a reactiondiffusion system modeling the cooperative interaction of two diffusion biological species in one space dimension. First we show the existence and uniqueness of a local classical solution, then we study the asymptotic behavior of the free boundary problem. Our results show that the free boundary problem admits a global solution if the i...
متن کاملThe Role of Critical Exponents in Blowup Theorems
In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation ut Au + up in RN with p > 1 and nonnegative initial values. Fujita showed that if 1 < p < 1 + 2IN, then the initial value problem had no nontrivial global solutions while if p > 1 + 2IN, there were nontrivial global solutions. This paper discusses simila...
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:
دوره شماره
صفحات -
تاریخ انتشار 2008