The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).
Canonical reference
American Mathematical Society, Providence, RI, 2010, pp
Canonical reference. 80% of citing Pith papers cite this work as background.
12
Pith papers citing it
Background
80% of classified citations
citation-role summary
background 4
method 1
citation-polarity summary
verdicts
UNVERDICTED 12representative citing papers
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
Quenched stochastic homogenization holds for elliptic equations under a coarse-grained ellipticity assumption on stationary ergodic coefficients, with a corollary on joint integrability of symmetric and skew-symmetric parts.
A mirror descent algorithm computes exact Wasserstein barycenters for mixed discrete and continuous input measures with convergence guarantees.
Numerical simulations of the Aw-Rascle-Zhang model on lattice networks produce scale-free congestion clusters with power-law size distributions and finite-size scaling.
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.
Matching-based AMG preconditioners deliver robust and scalable performance for solving large ill-conditioned systems from IgA discretizations in parallel HPC settings.
citing papers explorer
-
Spectral instability and non-uniqueness of mild solutions for the Keller-Segel system
The parabolic-elliptic Keller-Segel system is locally ill-posed in L^q(R^n) for n=3..9 and supercritical q in [1, n/2).
-
Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
-
Weighted mixed-norm estimates for circular averages and exceptional set estimates for the wave equation
Mixed-norm bounds for circular averages on α-dimensional fractals yield the first exceptional set estimates for Hölder regularity of linear wave solutions in R².
-
Layer Potential Methods for Doubly-Periodic Harmonic Functions
Develops and analyzes single- and double-layer potential operators for doubly-periodic harmonic functions on finitely-connected tori, proves compactness and boundary limits, constructs the null space for multiply-connected cases, and demonstrates spectral convergence for Dirichlet, Neumann, and Stek
-
Solving Inverse Parametrized Problems via Finite Elements and Extreme Learning Networks
A hybrid FEM and ELM framework for parameter-dependent PDEs derives existence, uniqueness, regularity, and error estimates for inverse problems in photoacoustic tomography.
-
Stochastic homogenization of coarse-grained elliptic equations
Quenched stochastic homogenization holds for elliptic equations under a coarse-grained ellipticity assumption on stationary ergodic coefficients, with a corollary on joint integrability of symmetric and skew-symmetric parts.
-
A Unified Approach for Computing Wasserstein Barycenters of Discrete and Continuous Measures
A mirror descent algorithm computes exact Wasserstein barycenters for mixed discrete and continuous input measures with convergence guarantees.
-
Scale-free congestion clusters in large-scale traffic networks: a continuum modeling study
Numerical simulations of the Aw-Rascle-Zhang model on lattice networks produce scale-free congestion clusters with power-law size distributions and finite-size scaling.
-
On a linear DG approximation of chemotaxis models with damping gradient nonlinearities
A novel linear upwind DG method for local and nonlocal chemotaxis models with nonlinear diffusion, attraction/repulsion, logistic growth and damping that preserves positivity and prevents numerical blow-up.
-
Well-posedness and regularity for seminlinear time-dependent second and fourth order in space equations
Existence and uniqueness of weak solutions are proved for the semilinear time-dependent equation with second or fourth order diffusion and cubic nonlinearity, for both smooth and rough initial data via Faedo-Galerkin and compactness methods.
-
Soliton-like solutions of the Camassa--Holm equation with variable coefficients and a small dispersion
The paper constructs asymptotic expansions for one-phase and two-phase soliton-like and peakon-like solutions of the variable-coefficient Camassa-Holm equation with small dispersion and proves their asymptotic accuracy.
-
Parallel matching-based AMG preconditioners for elliptic equations discretized by IgA
Matching-based AMG preconditioners deliver robust and scalable performance for solving large ill-conditioned systems from IgA discretizations in parallel HPC settings.