TY - JOUR AU - Garra, R. AU - Orsingher, E. TI - Euler–Poisson–Darboux equations and iterated fractional Brownian motions JF - BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA J2 - BOL SOC MAT MEX VL - 29 PY - 2023 IS - 3 SN - 1405-213X DO - 10.1007/s40590-023-00537-9 UR - https://m2.mtmt.hu/api/publication/34195117 ID - 34195117 LA - English DB - MTMT ER - TY - JOUR AU - Szigeti, Balázs Endre AU - Barna, Imre Ferenc AU - Barnaföldi, Gergely Gábor TI - The Formulation of Scaling Expansion in an Euler-Poisson Dark-Fluid Model JF - UNIVERSE J2 - UNIVERSE-BASEL VL - 9 PY - 2023 IS - 10 PG - 17 SN - 2218-1997 DO - 10.3390/universe9100431 UR - https://m2.mtmt.hu/api/publication/34237297 ID - 34237297 N1 - Export Date: 13 November 2023 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Pocsai, Mihály András AU - Barnaföldi, Gergely Gábor TI - Self-Similar Solutions of a Gravitating Dark Fluid JF - MATHEMATICS J2 - MATHEMATICS-BASEL VL - 10 PY - 2022 IS - 18 PG - 11 SN - 2227-7390 DO - 10.3390/math10183220 UR - https://m2.mtmt.hu/api/publication/33121241 ID - 33121241 N1 - Wigner Research Centre for Physics, 29-33 Konkoly–Thege Miklós Str, Budapest, 1121, Hungary Institute of Physics, Department of Physics, University of Pécs, 6 Ifjúság Útja, Pécs, 7624, Hungary Cited By :2 Export Date: 30 January 2024 Correspondence Address: Barna, I.F.; Wigner Research Centre for Physics, 29-33 Konkoly–Thege Miklós Str, Hungary; email: barna.imre@wigner.hu LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Pocsai, Mihály András AU - Matyas, Laszlo TI - Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths JF - MATHEMATICS J2 - MATHEMATICS-BASEL VL - 10 PY - 2022 IS - 13 PG - 16 SN - 2227-7390 DO - 10.3390/math10132311 UR - https://m2.mtmt.hu/api/publication/33017130 ID - 33017130 AB - We investigate a hydrodynamic equation system which-with some approximation-is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well. LA - English DB - MTMT ER - TY - JOUR AU - Matyas, L AU - Barna, Imre Ferenc TI - General self-similar solutions of diffusion equation and related constructions JF - ROMANIAN JOURNAL OF PHYSICS J2 - ROM J PHYS VL - 67 PY - 2022 IS - 1-2 PG - 16 SN - 1221-146X UR - https://m2.mtmt.hu/api/publication/32836601 ID - 32836601 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Kersner, Róbert TI - Reply to comment on ‘Heat conduction: a telegraph-type model with self-similar behavior of solutions’ (2010 J. Phys. A: Math. Theor. 43 375210) JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 54 PY - 2021 IS - 8 PG - 1 SN - 1751-8113 DO - 10.1088/1751-8121/aba91c UR - https://m2.mtmt.hu/api/publication/31891062 ID - 31891062 N1 - doc type - wos: editorial doi - REPLY Scopus: note TT: Reply to comment on ‘Heat conduction: a telegraph-type model with self-similar behavior of solutions’ (2010 J. Phys. A: Math. Theor. 43 375210) LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Mátyás, L. TI - Analytic solutions of a two-fluid hydrodynamic model JF - MATHEMATICAL MODELLING AND ANALYSIS J2 - MATH MODEL ANAL VL - 26 PY - 2021 IS - 4 SP - 582 EP - 590 PG - 9 SN - 1392-6292 DO - 10.3846/mma.2021.13637 UR - https://m2.mtmt.hu/api/publication/32499987 ID - 32499987 LA - English DB - MTMT ER - TY - JOUR AU - Nagy, Ádám AU - OMLE, ISSA AU - AL-JANABI, HUMAM KAREEM JALGHAF AU - Kovács, Endre AU - Barna, Imre Ferenc AU - Vadászné Bognár, Gabriella TI - Stable, Explicit, Leapfrog-Hopscotch Algorithms for the Diffusion Equation JF - COMPUTATION J2 - COMPUTATION VL - 9 PY - 2021 IS - 8 PG - 25 SN - 2079-3197 DO - 10.3390/computation9080092 UR - https://m2.mtmt.hu/api/publication/32174243 ID - 32174243 AB - In this paper, we construct novel numerical algorithms to solve the heat or diffusion equation. We start with 105 different leapfrog-hopscotch algorithm combinations and narrow this selection down to five during subsequent tests. We demonstrate the performance of these top five methods in the case of large systems with random parameters and discontinuous initial conditions, by comparing them with other methods. We verify the methods by reproducing an analytical solution using a non-equidistant mesh. Then, we construct a new nontrivial analytical solution containing the Kummer functions for the heat equation with time-dependent coefficients, and also reproduce this solution. The new methods are then applied to the nonlinear Fisher equation. Finally, we analytically prove that the order of accuracy of the methods is two, and present evidence that they are unconditionally stable. LA - English DB - MTMT ER - TY - JOUR AU - Nagy, Ádám AU - Saleh, Mahmoud AU - OMLE, ISSA AU - AL-JANABI, HUMAM KAREEM JALGHAF AU - Kovács, Endre TI - New Stable, Explicit, Shifted-Hopscotch Algorithms for the Heat Equation JF - MATHEMATICAL AND COMPUTATIONAL APPLICATIONS J2 - MATH COMPUT APPL VL - 26 PY - 2021 IS - 3 PG - 23 SN - 1300-686X DO - 10.3390/mca26030061 UR - https://m2.mtmt.hu/api/publication/32163099 ID - 32163099 LA - English DB - MTMT ER - TY - JOUR AU - Pantokratoras, A. TI - Comment on ‘Heat conduction: A telegraph-type model with self-similar behavior of solutions’ JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 54 PY - 2021 IS - 8 PG - 2 SN - 1751-8113 DO - 10.1088/1751-8121/aba91e UR - https://m2.mtmt.hu/api/publication/31946526 ID - 31946526 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Vadászné Bognár, Gabriella AU - Guedda, M. AU - Mátyás, L. AU - Hriczó, Krisztián TI - Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms JF - MATHEMATICAL MODELLING AND ANALYSIS J2 - MATH MODEL ANAL VL - 25 PY - 2020 IS - 2 SP - 241 EP - 256 PG - 16 SN - 1392-6292 DO - 10.3846/mma.2020.10459 UR - https://m2.mtmt.hu/api/publication/31272217 ID - 31272217 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Vadászné Bognár, Gabriella AU - Mátyás, László AU - Guedda, M. AU - Hriczó, Krisztián TI - Analytic solutions of the two-dimensional kardar-parisi-zhang growing equation JF - AIP CONFERENCE PROCEEDINGS J2 - AIP CONF PROC VL - 2293 PY - 2020 PG - 4 SN - 0094-243X DO - 10.1063/5.0027197 UR - https://m2.mtmt.hu/api/publication/31794717 ID - 31794717 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Matyas, L AU - Pocsai, Mihály András TI - Self-similar analysis of a viscous heated Oberbeck-Boussinesq flow system JF - FLUID DYNAMICS RESEARCH J2 - FLUID DYN RES VL - 52 PY - 2020 IS - 1 PG - 11 SN - 0169-5983 DO - 10.1088/1873-7005/ab720c UR - https://m2.mtmt.hu/api/publication/31272223 ID - 31272223 LA - English DB - MTMT ER - TY - JOUR AU - Garra, R. AU - Orsingher, E. AU - Shishkina, E. L. TI - Solutions to Non-linear Euler-Poisson-Darboux Equations by Means of Generalized Separation of Variables JF - LOBACHEVSKII JOURNAL OF MATHEMATICS J2 - LOBACHEVSKII J MATHEMATICS VL - 40 PY - 2019 IS - 5 SP - 640 EP - 647 PG - 8 SN - 1818-9962 DO - 10.1134/S1995080219050093 UR - https://m2.mtmt.hu/api/publication/31098710 ID - 31098710 N1 - Department of Statistical Sciences, Sapienza University of Rome, Rome, 00185, Italy Applied Mathematics, Informatics and Mechanics Faculty, Voronezh State University, Voronezh, 394006, Russian Federation Export Date: 18 February 2022 Correspondence Address: Garra, R.; Department of Statistical Sciences, Italy; email: roberto.garra@sbai.uniroma1.it AB - This paper examines solutions to some non-linear equations which generalize well-known equations such as the Euler-Poisson-Darboux equation, the Kolmogorov-Petrovsky-Piskunov equation and telegraph-type equations. The method of generalized separation of variables is here used to derive new exact solutions to these equations. LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Pocsai, Mihály András AU - Mátyás, László TI - Self-Similarity Analysis of the Nonlinear Schrodinger Equation in the Madelung Form JF - ADVANCES IN MATHEMATICAL PHYSICS J2 - ADV MATH PHYS VL - 2018 PY - 2018 PG - 5 SN - 1687-9120 DO - 10.1155/2018/7087295 UR - https://m2.mtmt.hu/api/publication/30307727 ID - 30307727 AB - In the present study a particular case of Gross-Pitaevskii or nonlinear Schrodinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case. LA - English DB - MTMT ER - TY - CHAP AU - Barna, Imre Ferenc ED - Campos, Denise TI - Self-similar analysis of various Navier-stokes equations in two or three dimensions T2 - Handbook on Navier-Stokes Equations: Theory and Applied Analysis PB - Nova Science Publishers CY - Hauppauge, New York SN - 9781536102925 PY - 2017 SP - 275 EP - 304 PG - 30 UR - https://m2.mtmt.hu/api/publication/3280035 ID - 3280035 LA - English DB - MTMT ER - TY - JOUR AU - Garra, R AU - Orsingher, E TI - Random flights related to the Euler-Poisson - Darboux equation JF - MARKOV PROCESSES AND RELATED FIELDS J2 - MARKOV PROCESS RELAT FIELDS VL - 22 PY - 2016 SP - 87 EP - 110 PG - 24 SN - 1024-2953 UR - https://m2.mtmt.hu/api/publication/26093126 ID - 26093126 N1 - Cited By :12 Export Date: 18 February 2022 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Mátyás, László TI - Analytic solutions for the three-dimensional compressible Navier-Stokes equation JF - FLUID DYNAMICS RESEARCH J2 - FLUID DYN RES VL - 46 PY - 2014 IS - 5 PG - 10 SN - 0169-5983 DO - 10.1088/0169-5983/46/5/055508 UR - https://m2.mtmt.hu/api/publication/2758967 ID - 2758967 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc TI - Self-similar shock wave solutions of the nonlinear Maxwell equations JF - LASER PHYSICS J2 - LASER PHYS VL - 24 PY - 2014 IS - 8 PG - 5 SN - 1054-660X DO - 10.1088/1054-660X/24/8/086002 UR - https://m2.mtmt.hu/api/publication/2839369 ID - 2839369 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Mátyás, László TI - Analitic Solutions for the one-dimensional compressible Euler equarion with heat conduction with different kind of equation of states JF - MISKOLC MATHEMATICAL NOTES J2 - MISKOLC MATH NOTES VL - 14 PY - 2013 IS - 3 SP - 785 EP - 799 PG - 15 SN - 1787-2405 DO - 10.18514/mmn.2013.694 UR - https://m2.mtmt.hu/api/publication/2491790 ID - 2491790 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc TI - A general telegraph-type model for heat conduction with self-similar behaviour of solutions JF - LASERS IN ENGINEERING J2 - LASER ENG VL - 24 PY - 2013 IS - 1-2 SP - 95 EP - 104 PG - 10 SN - 0898-1507 UR - https://m2.mtmt.hu/api/publication/2210078 ID - 2210078 LA - English DB - MTMT ER - TY - JOUR AU - Makai, Mihály TI - Remarks on the Speed of Heat Waves JF - TRANSPORT THEORY AND STATISTICAL PHYSICS J2 - TRANSPORT THEOR STAT PHYS VL - 41 PY - 2012 SP - 245 EP - 264 PG - 20 SN - 0041-1450 DO - 10.1080/00411450.2012.671220 UR - https://m2.mtmt.hu/api/publication/2694888 ID - 2694888 N1 - Admin megjegyzés-24615980 #JournalID1# Name: TRANSPORT THEOR STAT ISSN: 0041-1450 #JournalID2# LA - English DB - MTMT ER - TY - JOUR AU - Barna, I F AU - Kersner, Róbert TI - Heat conduction. A telegraph-type model with self-similar behavior of solutions II TS - A telegraph-type model with self-similar behavior of solutions II JF - ADVANCED STUDIES IN THEORETICAL PHYSICS J2 - ADV STUDIES VL - 5 PY - 2011 IS - 1-4 SP - 193 EP - 205 PG - 13 SN - 1313-1311 UR - https://m2.mtmt.hu/api/publication/1756137 ID - 1756137 AB - In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210) we introduced a modified Fourier-Cattaneo law and derived a nonautonomous telegraph-type heat conduction equation which has desirable self-similar solution. Now we present a detailed in-depth analysis of this model and discuss additional analytic solutions for different parameters. The solutions have a very rich and interesting mathematical structure due to various special functions. LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc TI - Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation. https://m2.mtmt.hu/frontend/resources/images/open.png TS - https://m2.mtmt.hu/frontend/resources/images/open.png JF - COMMUNICATIONS IN THEORETICAL PHYSICS J2 - COMMUN THEOR PHYS VL - 56 PY - 2011 IS - 4 SP - 745 EP - 750 PG - 6 SN - 0253-6102 DO - 10.1088/0253-6102/56/4/25 UR - https://m2.mtmt.hu/api/publication/1868217 ID - 1868217 AB - In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches. LA - English DB - MTMT ER - TY - JOUR AU - Makai, Mihály TI - On the speed of heat waves JF - EUROPHYSICS LETTERS J2 - EUROPHYS LETT VL - 96 PY - 2011 IS - 4 SN - 0295-5075 DO - 10.1209/0295-5075/96/40010 UR - https://m2.mtmt.hu/api/publication/1871235 ID - 1871235 AB - We revisit the problem of heat conductance and diffusion, two remarkable transport processes characterized by instantaneous actions. We show that the assumption of local thermal equilibrium sets a limit to the speed of change in the distribution function of a statistical system S. A statistical system consists of a large number of components, and its state is changed through a large number if interactions among its components. A macroscopic phenomenon is obtained by averaging, thus it would be rather unexpected if any macroscopic phenomenon would exhibit a speed faster than the change rate of the distribution function itself. Using Onsager's approximation, we show that the balance equations of the extensive parameters also have solutions with finite velocities involved. At the same time the infinite speed is obtainable when second-order terms are neglected. We show how the presented technique is applied in plasma physics to determine the speeds of transport processes in fusion plasmas. Copyright (C) EPLA, 2011 LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Kersner, Róbert TI - Heat conduction: a telegraph-type model with self-similar behavior of solutions JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 43 PY - 2010 IS - 37 PG - 6 SN - 1751-8113 DO - 10.1088/1751-8113/43/37/375210 UR - https://m2.mtmt.hu/api/publication/1428953 ID - 1428953 LA - English DB - MTMT ER - TY - JOUR AU - Gilding, B H AU - Kersner, Róbert TI - A fisher/KPP-type equation with density-dependent diffusion and convection: Travelling-wave solutions JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL J2 - J PHYS A-MATH GEN VL - 38 PY - 2005 IS - 15 SP - 3367 EP - 3379 PG - 13 SN - 0305-4470 DO - 10.1088/0305-4470/38/15/009 UR - https://m2.mtmt.hu/api/publication/1756234 ID - 1756234 AB - This paper concerns processes described by a nonlinear partial differential equation that is an extension of the Fisher and KPP equations including density-dependent diffusion and nonlinear convection. The set of wave speeds forwhich the equation admits a wavefront connecting its stable and unstable equilibrium states is characterized. There is a minimal wave speed. For this wave speed there is a unique wavefront which can be found explicitly. It displays a sharp propagation front. For all greater wave speeds there is a unique wavefront which does not possess this property. For such waves, the asymptotic behaviour as the equilibrium states are approached is determined. © 2005 IOP Publishing Ltd. LA - English DB - MTMT ER - TY - JOUR AU - Gilding, B H AU - Kersner, Róbert TI - Instantaneous extinction, step discontinuities and blow-up JF - NONLINEARITY J2 - NONLINEARITY VL - 16 PY - 2003 IS - 3 SP - 843 EP - 854 PG - 12 SN - 0951-7715 DO - 10.1088/0951-7715/16/3/304 UR - https://m2.mtmt.hu/api/publication/1756217 ID - 1756217 N1 - WoS:hiba:000183174000005 2019-03-03 10:34 cikkazonosító nem egyezik AB - This note concerns reaction-diffusion processes which display remarkable behaviour. Everywhere the concentration, density or temperature exceeds some critical level until at some moment in time it decreases to the critical level at one point in space. At this instant, the complete profile immediately drops to the critical level at every point in space, and then remains there. LA - English DB - MTMT ER - TY - JOUR AU - Kamin, S AU - Kersner, Róbert AU - Tesei, A TI - On the Cauchy problem for a class of parabolic equations with variable density JF - RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI J2 - REND LINCEI-MAT APPL VL - 9 PY - 1998 IS - 4 SP - 279 EP - 298 PG - 20 SN - 1120-6330 UR - https://m2.mtmt.hu/api/publication/161626 ID - 161626 LA - English DB - MTMT ER - TY - JOUR AU - Kersner, Róbert AU - Vicsek, Tamásné TI - Travelling waves and dynamic scaling in a singular interface equation. analytic results TS - analytic results JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL J2 - J PHYS A-MATH GEN VL - 30 PY - 1997 IS - 7 SP - 2457 EP - 2465 PG - 9 SN - 0305-4470 DO - 10.1088/0305-4470/30/7/024 UR - https://m2.mtmt.hu/api/publication/161281 ID - 161281 LA - English DB - MTMT ER - TY - JOUR AU - Galaktionov, VA AU - Kersner, Róbert AU - Vazquez, JL TI - Asymptotic behaviour for an equation of superslow diffusion in a bounded domain JF - ASYMPTOTIC ANALYSIS J2 - ASYMPTOTIC ANAL VL - 8 PY - 1994 SP - 237 EP - 246 PG - 10 SN - 0921-7134 UR - https://m2.mtmt.hu/api/publication/160250 ID - 160250 LA - English DB - MTMT ER - TY - JOUR AU - Kamin, S AU - Kersner, Róbert TI - Disappearence of interfaces in finite time JF - MECCANICA J2 - MECCANICA VL - 28 PY - 1993 SP - 117 EP - 120 PG - 4 SN - 0025-6455 DO - 10.1007/BF01020323 UR - https://m2.mtmt.hu/api/publication/159915 ID - 159915 LA - English DB - MTMT ER - TY - JOUR AU - Kersner, Róbert AU - Nicolosi, F TI - On the free boundaries in a nonlinear diffusion-convection problem with positive initial conditions JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 16 PY - 1991 IS - 6 SP - 543 EP - 552 PG - 10 SN - 0362-546X DO - 10.1016/0362-546X(91)90027-X UR - https://m2.mtmt.hu/api/publication/1788516 ID - 1788516 LA - English DB - MTMT ER - TY - JOUR AU - Kersner, Róbert AU - De Mottoni, P TI - Support properties of non-negative solutions of a degenerate logistic equation JF - NONLINEARITY J2 - NONLINEARITY VL - 3 PY - 1990 IS - 2 SP - 453 EP - 474 PG - 22 SN - 0951-7715 DO - 10.1088/0951-7715/3/2/009 UR - https://m2.mtmt.hu/api/publication/1788517 ID - 1788517 N1 - WoS:hiba:A1990DK63100009 2019-03-03 10:36 cikkazonosító nem egyezik AB - The authors study a degenerate parabolic equation in one space variable, whose coefficients depend on space and time. Focussing on certain classes of solutions, they point out a variety of support shapes, and they discuss their dependency on specified parameters, such as the size of the initial support. LA - English DB - MTMT ER -