𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Critical Exponents of Fujita Type for Inhomogeneous Parabolic Equations and Systems

✍ Scribed by C Bandle; H.A Levine; Qi S Zhang

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
176 KB
Volume
251
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the large-time behavior of sign-changing solutions of inhomogeneous parabolic equations and systems. For example, for u t = u + u p + w x in R n Γ— 0 T , we show the following: If n β‰₯ 3 and R n w x dx > 0 and 1 < p ≀ n/ n -2 , then all solutions blow up in finite time, while if p > n/ n -2 there are both global and nonglobal solutions. We show by example that global solutions exist for all p > 1 and w satisfying R n w x dx < 0. When n = 1 2 and R n w x dx > 0, no solution can exist for all time. Extensions of the above result to various geometries and some other problems are indicated.

πŸ“œ SIMILAR VOLUMES

On critical exponents for some quasiline
On critical exponents for some quasilinear parabolic equations
✍ Howard A. Levine; Gary M. Lieberman; Peter Meier πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 381 KB πŸ‘ 1 views

## Abstract We study the Cauchy problem for the quasilinear parabolic equation magnified image where __p__ > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with βˆ’ β©½ __s__Οˆβ€²(__s__)/ψ(__s__) β©½ ΞΈ for some ΞΈ > 0. If 1 < __p__ < 1 + 2/__N__, there are no global positive solutions, wherea

Critical Fujita exponents for a class of
Critical Fujita exponents for a class of nonlinear convection–diffusion equations
✍ Wei Guo; Zejia Wang; Runmei Du; Lishu Wen πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 173 KB πŸ‘ 1 views

## Communicated by M. Fila In this paper, we establish the blow-up theorems of Fujita type for a class of homogeneous Neumann exterior problems of quasilinear convection-diffusion equations. The critical Fujita exponents are determined and it is shown that the exponents belong to the blow-up case

On Critical Exponents for a Semilinear P
On Critical Exponents for a Semilinear Parabolic System Coupled in an Equation and a Boundary Condition
✍ Marek Fila; Howard A. Levine πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 242 KB

In this paper, we consider the system q 1 1 0 0 and bounded. We prove that if pq F 1 every nonnegative solution is global. When Ž . Ž . Ž . Ž . pq ) 1 we let ␣ s p q 2 r2 pq y 1 , ␀ s 2 q q 1 r2 pq y 1 . We show that if Ž . Ž . max ␣, ␀ ) Nr2 or max ␣, ␀ s Nr2 and p, q G 1, then all nontrivial nonne

Critical exponents for semilinear equati
Critical exponents for semilinear equations of mixed elliptic-hyperbolic and degenerate types
✍ Daniela Lupo; Kevin R. Payne πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 222 KB

## Abstract For semilinear Gellerstedt equations with Tricomi, Goursat or Dirichlet boundary conditions we prove Pohozaev type identities and derive non existence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical exponent phenomenon o