@article{MTMT:34779145,
	title = {Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy},
	url = {https://m2.mtmt.hu/api/publication/34779145},
	author = {Andrade, P.D.S. and dos, Prazeres D.S. and Santos, M.S.},
	doi = {10.1088/1361-6544/ad2c22},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34779145},
	issn = {0951-7715},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34761032,
	title = {Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates},
	url = {https://m2.mtmt.hu/api/publication/34761032},
	author = {Longo, I.P. and Núñez, C. and Obaya, R.},
	doi = {10.1088/1361-6544/ad2eb9},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34761032},
	issn = {0951-7715},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34672433,
	title = {Modeling the interplay of oscillatory synchronization and aggregation via cell-cell adhesion},
	url = {https://m2.mtmt.hu/api/publication/34672433},
	author = {Glimm, Tilmann and Gruszka, Daniel},
	doi = {10.1088/1361-6544/ad237a},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34672433},
	issn = {0951-7715},
	abstract = {We present a model of systems of cells with intracellular oscillators ('clocks'). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion and adhere to each other. The adhesion strength between neighbors depends on their clock phases in addition to a constant baseline strength. The oscillators are linked via Kuramoto-type local interactions. The model is an advection-diffusion partial differential equation with nonlocal advection terms. We demonstrate that synchronized states correspond to Dirac-delta measure solutions of a weak version of the equation. To analyze the complex interplay of aggregation and synchronization, we then perform a linear stability analysis of the incoherent, spatially uniform state. This lets us classify possibly emerging patterns depending on model parameters. Combining these results with numerical simulations, we determine a range of possible far-from equilibrium patterns when baseline adhesion strength is zero: There is aggregation into separate synchronized clusters with or without global synchrony; global synchronization without aggregation; or unexpectedly a 'phase wave' pattern characterized by spatial gradients of clock phases. A 2D Lattice-Gas Cellular Automaton model confirms and illustrates these results.},
	keywords = {BEHAVIOR; EVOLUTION; NETWORK; Movement; POPULATIONS; SYNCHRONIZATION; pattern formation; cell aggregation; Mathematics, Applied; advection-diffusion equations; lattice-gas cellular automata},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34629019,
	title = {Glimm's method and density of wild data for the Euler system of gas dynamics},
	url = {https://m2.mtmt.hu/api/publication/34629019},
	author = {Chiodaroli, Elisabetta and Feireisl, Eduard},
	doi = {10.1088/1361-6544/ad1cbd},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34629019},
	issn = {0951-7715},
	keywords = {Riemann problem; Convex integration; Euler system of gas dynamics; wild data},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34614055,
	title = {Boundary asymptotics of non-intersecting Brownian motions: Pearcey, Airy and a transition},
	url = {https://m2.mtmt.hu/api/publication/34614055},
	author = {Neuschel, Thorsten and Venker, Martin},
	doi = {10.1088/1361-6544/ad1dbc},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34614055},
	issn = {0951-7715},
	abstract = {We study n non-intersecting Brownian motions, corresponding to the eigenvalues of an n x n Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process close to merging points, the Airy line ensemble at edges and a novel determinantal process describing the transition from the Pearcey process to the Airy line ensemble. The three cases are distinguished by a remarkably simple integral condition. Our results hold under very mild assumptions, in particular we do not require any kind of convergence of the initial configuration as n ->infinity . Applications to largest eigenvalues of macro- and mesoscopic bulks and to random initial configurations are given.},
	keywords = {TRANSITION; UNIVERSALITY; RANDOM MATRICES; Dyson's Brownian motion; Airy line ensemble; Pearcey process},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34609430,
	title = {Cusps in heavy billiards},
	url = {https://m2.mtmt.hu/api/publication/34609430},
	author = {Hasselblatt, Boris and Kim, Ki Yeun and Levi, Mark},
	doi = {10.1088/1361-6544/ad1496},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34609430},
	issn = {0951-7715},
	abstract = {We consider billiards with cusps and with gravity pulling the particle into the cusp. We discover an adiabatic invariant in this context; it turns out that the invariant is in form almost identical to the Clairaut integral (angular momentum) for surfaces of revolution. We also approximate the bouncing motion of a particle near a cusp by smooth motion governed by a differential equation-which turns out to be identical to the differential equation governing geodesic motion on a surface of revolution. We also show that even in the presence of gravity pulling into a cusp of a billiard table, only the direct-hit orbit reaches the tip of the cusp. Finally, we provide an estimate of the maximal depth to which a particle penetrates the cusp before being ejected from it.},
	keywords = {BILLIARDS; CUSP; Adiabatic invariant; 70; 37},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34629736,
	title = {Invariant measures for a stochastic nonlinear and damped 2D Schrödinger equation},
	url = {https://m2.mtmt.hu/api/publication/34629736},
	author = {Brzezniak, Zdzislaw and Ferrario, Benedetta and Zanella, Margherita},
	doi = {10.1088/1361-6544/ad0f3a},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34629736},
	issn = {0951-7715},
	keywords = {tightness; nonlinear Schrodinger equation; Invariant measure; Multiplicative noise; Galerkin approximation; pathwise uniqueness; sequential weak Feller},
	year = {2024},
	eissn = {1361-6544},
	orcid-numbers = {Brzezniak, Zdzislaw/0000-0001-8731-6523}
}

@article{MTMT:34605571,
	title = {The most probable transition paths of stochastic dynamical systems: a sufficient and necessary characterisation},
	url = {https://m2.mtmt.hu/api/publication/34605571},
	author = {Huang, Yuanfei and Huang, Qiao and Duan, Jinqiao},
	doi = {10.1088/1361-6544/ad0ffe},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34605571},
	issn = {0951-7715},
	abstract = {The most probable transition paths (MPTPs) of a stochastic dynamical system are the global minimisers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange (EL) equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterisation for the MPTPs of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the MPTPs are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager-Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler's model, the first-order differential equations determining the MPTPs are shown analytically to imply the EL equations of the Onsager-Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results.},
	keywords = {stochastic dynamical systems; most probable transition paths; Markovian bridges; Onsager-Machlup action functional},
	year = {2024},
	eissn = {1361-6544},
	orcid-numbers = {Duan, Jinqiao/0000-0002-2077-990X}
}

@article{MTMT:34581140,
	title = {Spectrality of random convolutions generated by finitely many Hadamard triples},
	url = {https://m2.mtmt.hu/api/publication/34581140},
	author = {Li, Wenxia and Miao, Jun Jie and Wang, Zhiqiang},
	doi = {10.1088/1361-6544/ad0d70},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {37},
	unique-id = {34581140},
	issn = {0951-7715},
	abstract = {Let {(Nj,Bj,Lj):1 <= j <= m} be finitely many Hadamard triples in R . Given a sequence of positive integers {nk}k=1 infinity and omega=(omega k)k=1 infinity is an element of{1,2, horizontal ellipsis ,m}N , let mu omega,{nk} be the infinite convolution given by mu omega,nk=delta N omega 1-n1B omega 1*delta N omega 1-n1N omega 2-n2B omega 2*MIDLINE HORIZONTAL ELLIPSIS*delta N omega 1-n1N omega 2-n2MIDLINE HORIZONTAL ELLIPSISN omega k-nkB omega k*MIDLINE HORIZONTAL ELLIPSIS.In order to study the spectrality of mu omega,{nk} , we first show the spectrality of general infinite convolutions generated by Hadamard triples under the equi-positivity condition. Then by using the integral periodic zero set of Fourier transform we show that if gcd(Bj-Bj)=1 for 1 <= j <= m , then all infinite convolutions mu omega,{nk} are spectral measures. This implies that we may find a subset Lambda omega,{nk}subset of R such that {e lambda(x)=e2 pi i lambda x:lambda is an element of Lambda omega,{nk}} forms an orthonormal basis for L2(mu omega,{nk}) .},
	keywords = {Spectral measure; Orthonormal basis; Infinite convolution; equi-positivity},
	year = {2024},
	eissn = {1361-6544}
}

@article{MTMT:34313500,
	title = {On zonal steady solutions to the 2D Euler equations on the rotating unit sphere},
	url = {https://m2.mtmt.hu/api/publication/34313500},
	author = {Nualart, Marc},
	doi = {10.1088/1361-6544/acec26},
	journal-iso = {NONLINEARITY},
	journal = {NONLINEARITY},
	volume = {36},
	unique-id = {34313500},
	issn = {0951-7715},
	abstract = {The present paper studies the structure of the set of stationary solutions to the incompressible Euler equations on the rotating unit sphere that are near two basic zonal flows: the zonal Rossby-Haurwitz solution of degree 2 and the zonal rigid rotation Y-1(0) along the polar axis. We construct a new family of non-zonal steady solutions arbitrarily close in analytic regularity to the second degree zonal Rossby-Haurwitz stream function, for any given rotation of the sphere. This shows that any non-linear inviscid damping to a zonal flow cannot be expected for solutions near this Rossby-Haurwitz solution. On the other hand, we prove that, under suitable conditions on the rotation of the sphere, any stationary solution close enough to the rigid rotation zonal flow Y-1(0) must itself be zonal, witnessing some sort of rigidity inherited from the equation, the geometry of the sphere and the base flow. Nevertheless, when the conditions on the rotation of the sphere fail, the set of solutions is much richer and we are able to prove the existence of both explicit stationary and travelling wave non-zonal solutions bifurcating from Y-1(0), in the same spirit as those emanating from the zonal Rossby-Haurwitz solution of degree 2.},
	keywords = {Euler equations; zonal flows; STATIONARY FLOWS},
	year = {2023},
	eissn = {1361-6544},
	pages = {4981-5006},
	orcid-numbers = {Nualart, Marc/0000-0003-3697-3421}
}