117 citations · 882 across the 65 of their papers we have counts for
8 papers · 1 filter
The Hawking-Penrose singularity theorem for -Lorentzian metrics
Michael Kunzinger, Argam Ohanyan, Benedict Schinnerl +1
We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity . For metrics of such low regularity, two m…
The Hawking-Penrose singularity theorem for -Lorentzian metrics
Melanie Graf, James D. E. Grant, Michael Kunzinger +1
We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^…
Singular reduction modules of differential equations
Vaycheslav M. Boyko, Michael Kunzinger, Roman O. Popovych
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation…
Generalized conditional symmetries of evolution equations
Michael Kunzinger, Roman O. Popovych
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as t…
Is a nonclassical symmetry a symmetry?
Michael Kunzinger, Roman O. Popovych
Various versions of the definition of nonclassical symmetries existing in the literature are analyzed. Comparing properties of Lie and nonclassical symmetries leads to the conclusi…
Potential Conservation Laws
Michael Kunzinger, Roman O. Popovych
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characterist…
Conservation Laws and Potential Symmetries of Linear Parabolic Equations
Roman O. Popovych, Michael Kunzinger, Nataliya M. Ivanova
We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classifi…
Admissible Transformations and Normalized Classes of Nonlinear Schroedinger Equations
Roman O. Popovych, Michael Kunzinger, Homayoon Eshraghi
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normaliz…