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Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
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
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A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
We investigate the properties of solutions of a system of chemotaxis equations arising in the theory of reinforced random walks. Expand
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The Role of Critical Exponents in Blowup Theorems
  • H. Levine
  • Mathematics, Computer Science
  • SIAM Rev.
  • 1 June 1990
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
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The Role of Critical Exponents in Blow-Up Theorems: The Sequel
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 theExpand
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On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains
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 someExpand
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Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity
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
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Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
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 establishedExpand
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