A critical exponent in a degenerate parabolic equation

By Michael Winkler. 2002

93 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/04c59a564311ef07258832542ec3fe96bcd66257

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Boundedness and large time behavior in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion and general sensitivity (2015, unknown): “In view of the Gagliardo–Nirenberg inequality (see [33] for a version involving integrability exponents less than one) and (2.”
Cauchy problems of semilinear pseudo-parabolic equations ✩ (2009, result): “We refer to the survey papers [6,19], the recent works [1,20,21,25,32–36] and the references therein for a detailed account.”
A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up (2016, unknown): “We next invoke the Gagliardo-Nirenberg inequality [31] to find c1 > 0 such that with a := n n+1 we have ‖φ‖L1(Ω) ≤ c1‖∇φ‖L1(Ω)‖φ‖ L 1 2 (Ω) + c1‖φ‖ L 1 2 (Ω) for all φ ∈W (1,1)(Ω), and thereby obtain that”
Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops (2012, unknown): “[25] for a version involving L spaces with r < 1) provides c2 > 0 such that ( ∫ n ) 1 2 = np2 (2)L4 ≤ c2 ( np2 L2 · n p 2 L2 + n p 2 2 L 2 p )”
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion (2013, background): “[25] for a version involving L spaces with r < 1) to obtain C3 > 0 such that T ∫”
Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant (2012, background): “[20] for a version involving Lr space with r < 1) provides c2 > 0 such that”
Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system (2017, unknown): “In order to prepare an adequate estimation of the three rightmost summands herein, we invoke the Gagliardo-Nirenberg inequality (see [32] for a version suitable in the present case involving small summability powers) to find c3 > 0 such that ‖ψ‖ 2(p+1) p L 2(p+1) p (Ω) ≤ c3‖∇ψ‖ 2 L2(Ω)‖ψ‖ 2 p L 2 p ”
Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion (2015, unknown): “It follows from the Gagliardo-Nirenberg inequality [25] that ‖nε + ε‖ L 6 5 (Ω) = ∥ ∥ ∥ (nε + ε) m 2 ∥ ∥ ∥ 2 m L 12 5m (Ω) ≤ C2 ( ∥”
Fujita-type results for the degenerate parabolic equations on the Heisenberg groups (2023, unknown): “In [28] Winkler extended the results of [10] by taking the more general k ≥ 1 in (1.5).”