@article{MTMT:34415352,
	title = {The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling},
	url = {https://m2.mtmt.hu/api/publication/34415352},
	author = {Pereira, M and Kulcsar, Balazs and Lipták, György and Kovács, Mihály and Szederkényi, Gábor},
	doi = {10.1016/j.trc.2023.104435},
	journal-iso = {TRANSPORT RES C-EMER},
	journal = {TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES},
	volume = {158},
	unique-id = {34415352},
	issn = {0968-090X},
	year = {2024},
	eissn = {1879-2359},
	orcid-numbers = {Pereira, M/0000-0002-7899-2690; Kovács, Mihály/0000-0001-7977-9114; Szederkényi, Gábor/0000-0003-4199-6089}
}

@article{MTMT:34646798,
	title = {REGULARITY AND NUMERICAL APPROXIMATION OF FRACTIONAL ELLIPTIC DIFFERENTIAL EQUATIONS ON COMPACT METRIC GRAPHS},
	url = {https://m2.mtmt.hu/api/publication/34646798},
	author = {Bolin, David and Kovács, Mihály and Kumar, Vivek and Simas, Alexandre B.},
	doi = {10.1090/mcom/3929},
	journal-iso = {MATH COMPUT},
	journal = {MATHEMATICS OF COMPUTATION},
	unique-id = {34646798},
	issn = {0025-5718},
	year = {2023},
	eissn = {1088-6842},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114}
}

@article{MTMT:34069695,
	title = {Nonlinear semigroups for nonlocal conservation laws},
	url = {https://m2.mtmt.hu/api/publication/34069695},
	author = {Kovács, Mihály and Vághy, Mihály András},
	doi = {10.1007/s42985-023-00249-9},
	journal-iso = {Partial Differ. Equ. Appl.},
	journal = {Partial Differential Equations and Applications},
	volume = {4},
	unique-id = {34069695},
	issn = {2662-2963},
	year = {2023},
	eissn = {2662-2971},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114}
}

@article{MTMT:34048342,
	title = {On the parabolic Cauchy problem for quantum graphs with vertex noise},
	url = {https://m2.mtmt.hu/api/publication/34048342},
	author = {Kovács, Mihály and Sikolya, Eszter},
	doi = {10.1214/23-EJP962},
	journal-iso = {ELECTRON J PROBAB},
	journal = {ELECTRONIC JOURNAL OF PROBABILITY},
	volume = {28},
	unique-id = {34048342},
	issn = {1083-6489},
	abstract = {We investigate the parabolic Cauchy problem associated with quantum graphs includ-ing Lipschitz or polynomial type nonlinearities and additive Gaussian noise perturbed vertex conditions. The vertex conditions are the standard continuity and Kirchhoff assumptions in each vertex. In the case when only Kirchhoff conditions are perturbed, we can prove existence and uniqueness of a mild solution with continuous paths in the standard state space 9-L of square integrable functions on the edges. We also show that the solution is Markov and Feller. Furthermore, assuming that the vertex values of the normalized eigenfunctions of the self-adjoint operator governing the problem are uniformly bounded, we show that the mild solution has continuous paths in the fractional domain space associated with the Hamiltonian operator, 9-L & alpha; for & alpha; < 14. This is the case when the Hamiltonian operator is the standard Laplacian perturbed by a potential. We also show that if noise is present in both type of vertex conditions, then the problem admits a mild solution with continuous paths in the fractional domain space 9-L & alpha; with & alpha; < -14 only. These regularity results are the quantum graph ana-logues obtained by da Prato and Zabczyk [9] in case of a single interval and classical boundary Dirichlet or Neumann noise.},
	year = {2023},
	eissn = {1083-6489},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:32896300,
	title = {Approximation of SPDE covariance operators by finite elements: a semigroup approach},
	url = {https://m2.mtmt.hu/api/publication/32896300},
	author = {Kovács, Mihály and Lang, Annika and Petersson, Andreas},
	doi = {10.1093/imanum/drac020},
	journal-iso = {IMA J NUMER ANAL},
	journal = {IMA JOURNAL OF NUMERICAL ANALYSIS},
	volume = {43},
	unique-id = {32896300},
	issn = {0272-4979},
	abstract = {The problem of approximating the covariance operator of the mild solution to a linear stochastic partial differential equation is considered. An integral equation involving the semigroup of the mild solution is derived and a general error decomposition is proven. This formula is applied to approximations of the covariance operator of a stochastic advection-diffusion equation and a stochastic wave equation, both on bounded domains. The approximations are based on finite element discretizations in space and rational approximations of the exponential function in time. Convergence rates are derived in the trace class and Hilbert-Schmidt norms with numerical simulations illustrating the results.},
	keywords = {finite element method; integral equations; covariance operators; Stochastic partial differential equations; stochastic advection-diffusion equations},
	year = {2023},
	eissn = {1464-3642},
	pages = {1324-1357},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114}
}

@article{MTMT:32813160,
	title = {Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise},
	url = {https://m2.mtmt.hu/api/publication/32813160},
	author = {Fahim, K. and Hausenblas, E. and Kovács, Mihály},
	doi = {10.1007/s40072-022-00250-0},
	journal-iso = {STOCHASTICS PARTIAL DIFFERENTIAL EQUATIONS},
	journal = {STOCHASTICS PARTIAL DIFFERENTIAL EQUATIONS: ANALYSIS AND COMPUTATIONS},
	volume = {11},
	unique-id = {32813160},
	issn = {2194-0401},
	year = {2023},
	eissn = {2194-041X},
	pages = {1044-1088},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114}
}

@article{MTMT:32811394,
	title = {Hilbert-Schmidt regularity of symmetric integral operators on bounded domains with applications to SPDE approximations},
	url = {https://m2.mtmt.hu/api/publication/32811394},
	author = {Kovács, Mihály and Lang, Annika and Petersson, Andreas},
	doi = {10.1080/07362994.2022.2053541},
	journal-iso = {STOCH ANAL APPL},
	journal = {STOCHASTIC ANALYSIS AND APPLICATIONS},
	volume = {41},
	unique-id = {32811394},
	issn = {0736-2994},
	abstract = {Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates are of the form of Hilbert-Schmidt norms of the integral operator and its square root, composed with fractional powers of an elliptic operator equipped with homogeneous boundary conditions of either Dirichlet or Neumann type. These types of estimates, which couple the regularity of the driving noise with the properties of the differential operator, have important implications for stochastic partial differential equations on bounded domains as well as their numerical approximations. The main tools used to derive the estimates are properties of reproducing kernel Hilbert spaces of functions on bounded domains along with Hilbert-Schmidt embeddings of Sobolev spaces. Both non-homogeneous and homogeneous kernels are considered. In the latter case, results in a general Schatten class norm are also provided. Important examples of homogeneous kernels covered by the results of the paper include the class of Matern kernels.},
	keywords = {interpolation; WAVE-EQUATION; Stochastic partial differential equations; Mathematics, Applied; Elliptic operators; Fast simulation; Integral operators; Reproducing kernel Hilbert spaces; WEAK-CONVERGENCE RATES},
	year = {2023},
	eissn = {1532-9356},
	pages = {564-590},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Lang, Annika/0000-0003-2661-533X}
}

@article{MTMT:33193060,
	title = {SURFACE FINITE ELEMENT APPROXIMATION OF SPHERICAL WHITTLE--MAT\\'ERN GAUSSIAN RANDOM FIELDS},
	url = {https://m2.mtmt.hu/api/publication/33193060},
	author = {Jansson, Erik and Kovács, Mihály and Lang, Annika},
	doi = {10.1137/21M1400717},
	journal-iso = {SIAM J SCI COMPUT},
	journal = {SIAM JOURNAL ON SCIENTIFIC COMPUTING},
	volume = {44},
	unique-id = {33193060},
	issn = {1064-8275},
	abstract = {Spherical Whittle--Mate'\rn Gaussian random fields are considered as solutions to fractional elliptic stochastic partial differential equations on the sphere. Approximation is done with surface finite elements. While the nonfractional part of the operator is solved by a recursive scheme, a quadrature of the Dunford-Taylor integral representation is employed for the fractional part. Strong error analysis is performed, and the computational complexity is bounded in terms of the accuracy. Numerical experiments for different choices of parameters confirm the theoretical findings.},
	year = {2022},
	eissn = {1095-7197},
	pages = {A825-A842},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Lang, Annika/0000-0003-2661-533X}
}

@article{MTMT:33124279,
	title = {Kinetic discretization of one-dimensional nonlocal flow models},
	url = {https://m2.mtmt.hu/api/publication/33124279},
	author = {Vághy, Mihály András and Kovács, Mihály and Szederkényi, Gábor},
	doi = {10.1016/j.ifacol.2022.09.073},
	journal-iso = {IFACOL},
	journal = {IFAC PAPERSONLINE},
	volume = {55},
	unique-id = {33124279},
	issn = {2405-8971},
	year = {2022},
	eissn = {2405-8963},
	pages = {67-72},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Szederkényi, Gábor/0000-0003-4199-6089}
}

@article{MTMT:32916676,
	title = {A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains},
	url = {https://m2.mtmt.hu/api/publication/32916676},
	author = {Baeumer, Boris and Kovács, Mihály and Parry, Matthew},
	doi = {10.1007/s13540-021-00013-z},
	journal-iso = {FRACT CALC APPL ANAL},
	journal = {FRACTIONAL CALCULUS AND APPLIED ANALYSIS},
	volume = {25},
	unique-id = {32916676},
	issn = {1311-0454},
	abstract = {We develop a finite difference approximation of order alpha for the alpha-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Grunwald scheme. In particular, approximate solutions to fractional diffusion equations preserve positivity. Furthermore, for the approximation of the solution to the skewed fractional heat equation on a bounded domain the new approximation scheme keeps its order alpha whereas the order of the Grunwald scheme reduces to order alpha - 1, contradicting the convergence rate results by Meerschaert and Tadjeran.},
	keywords = {Fractional calculus; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Fractional partial differential equations; Polylogarithm},
	year = {2022},
	eissn = {1314-2444},
	pages = {299-319},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Parry, Matthew/0000-0002-6588-0219}
}