TY - JOUR

T1 - Stabilization of solutions of the diffusion equation with a non-lipschitz reaction term

AU - Kuto, Kousuke

PY - 2001/8/1

Y1 - 2001/8/1

N2 - In this paper we are concerned with the reaction-diffusion equation ut = Δu + f(u) in a ball of RN with Dirichlet boundary condition. We assume that f satisfies the concave-convex condition. A typical example is f(u) = |u|q-1u + |u|p-1u (0 < q < 1 < p < (N+2)/(N-2)). First we obtain the complete structure of positive solutions to the stationary problem; Δφ + f(φ) = 0. Next we state the relations between this structure and time-depending behaviors of nonnegative solutions (global existence or blow up) to the non-stationary problem.

AB - In this paper we are concerned with the reaction-diffusion equation ut = Δu + f(u) in a ball of RN with Dirichlet boundary condition. We assume that f satisfies the concave-convex condition. A typical example is f(u) = |u|q-1u + |u|p-1u (0 < q < 1 < p < (N+2)/(N-2)). First we obtain the complete structure of positive solutions to the stationary problem; Δφ + f(φ) = 0. Next we state the relations between this structure and time-depending behaviors of nonnegative solutions (global existence or blow up) to the non-stationary problem.

KW - Blow up

KW - Comparison theorem

KW - Global solution

KW - Non-Lipschitzian nonlinearity

KW - Radially symmetric solution

KW - Reaction-diffusion equation

UR - http://www.scopus.com/inward/record.url?scp=0035425713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035425713&partnerID=8YFLogxK

U2 - 10.1016/S0362-546X(01)00223-1

DO - 10.1016/S0362-546X(01)00223-1

M3 - Conference article

AN - SCOPUS:0035425713

VL - 47

SP - 789

EP - 800

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 2

T2 - 3rd World Congres of Nonlinear Analysts

Y2 - 19 July 2000 through 26 July 2000

ER -