The global existence for diffusion equations with small delay

  • Yin Xunwu
  • Published 2010 in
    2010 International Conference on Future…

Abstract

In this article, we prove that for scalar dissipative delay-diffusion equations u<inf>t</inf> − Δu = ƒ (u(t),u(t −τ )) with a small delay, there exists a global mild solution. Our main theory is the fundamental theorem on sectorial operators in [5]. We choose A = −Δ,W = L<sup>2</sup>(Ω),D(Δ<sup>1 over 2</sup>)= H<inf>0</inf><sup>1</sup>(Ω). Imposing some… (More)

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