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Blow-up Theories for Semilinear Parabolic Equations
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In this paper, a review of elliptic theories and parabolic theories is presented, along with fixed point theorems and blow-up rates for evolution equations, as well as self-similar blowup solutions.Abstract:
1 Introduction.- 2 A review of elliptic theories.- 3 A review of parabolic theories.- 4 A review of fixed point theorems.-5 Finite time Blow-up for evolution equations.- 6 Steady-State solutions.- 7 Blow-up rate.- 8 Asymptotically self-similar blow-up solutions.- 9 One space variable caseread more
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Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States
Pavol Quittner,Philippe Souplet +1 more
TL;DR: In this article, the authors propose a model for solving the model elliptic problems and model parabolic problems. But their model is based on Equations with Gradient Terms (EGS).
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Global classical small-data solutions for a three-dimensional chemotaxis Navier–Stokes system involving matrix-valued sensitivities
Xinru Cao,Johannes Lankeit +1 more
TL;DR: In this paper, the coupled chemotaxis fluid system has global classical solutions if the initial data satisfy certain smallness conditions and give decay properties of these solutions, and the authors show that it has global-classical solutions with global classical decay properties.
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Global classical small-data solutions for a three-dimensional chemotaxis Navier-Stokes system involving matrix-valued sensitivities
Xinru Cao,Johannes Lankeit +1 more
TL;DR: In this paper, the coupled chemotaxis fluid system has global classical solutions if the initial data satisfy certain smallness conditions and give decay properties of these solutions, and the authors show that the solution is global classical.
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Dynamics for a two-species competition–diffusion model with two free boundaries
Jong-Shenq Guo,Chang-Hong Wu +1 more
TL;DR: In this paper, the authors studied the spreading and interaction of two competing species in a two-species competition-diffusion model with two free boundaries and provided some characterization of the spreading vanishing trichotomy.
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Bounds for the blowup time of the solutions to quasi-linear parabolic problems
Aiguo Bao,Xianfa Song +1 more
TL;DR: In this article, the lower and upper bounds of the blowup time of the solutions to quasi-linear parabolic problems subject to Dirichlet(or Neumann) boundary condition were obtained.