Let P and A be symmetric linear operators defined on a dense domain $D \subset H$, a (real) Hilbert space. Let $(x,Av) \geqq \lambda (x,x)$ for all $x \in D$ and some $\lambda > 0$ and $(x,Px) > 0$… Expand

In this article various extensions of an old result of Fujita are considered for the initial value problem for the reaction-diffusion equation $u_t = \Delta u + u^p$.Expand

Abstract In [ 27 ] Fujita showed that for positive solutions, the initial value problem (in R N ) for u t = Δ u + u p with p > 1 exhibited the following behavior: If p p c ≡ 1 + 2/ N , then the… Expand

In this paper we study the first initial-boundary value problem for ut = Au + uP in conical domains D = (0, oo) x Q c RN where Q c SN-I is an open connected manifold with boundary. We obtain some… Expand

Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region.… Expand

The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed by Judah Folkman in the early 1970s and subsequently established… Expand