Zobrazeno 1 - 10
of 264
pro vyhledávání: '"Oberguggenberger, Michael"'
The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic analysis.
Externí odkaz:
http://arxiv.org/abs/2409.17034
Autor:
Oberguggenberger, Michael
The paper addresses the question whether a random functional, a map from a set $E$ into the space of real-valued measurable functions on a probability space, has a measurable version with values in ${\mathbb R}^E$. Similarly, one may ask whether line
Externí odkaz:
http://arxiv.org/abs/2402.04926
Publikováno v:
Journal of Differential Equations 406 (2024), 302-317
This paper finds solutions to semilinear wave equations with strongly anomalous propagation of singularities. For very low Sobolev regularity we obtain solutions whose singular support propagates along any ray inside or outside the light cone. In one
Externí odkaz:
http://arxiv.org/abs/2302.13772
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 1406-1430
We compare two standard approaches to defining lower Ricci curvature bounds for Riemannian metrics of regularity below $C^2$. These are, on the one hand, the synthetic definition via weak displacement convexity of entropy functionals in the framework
Externí odkaz:
http://arxiv.org/abs/2207.03715
Publikováno v:
In Journal of Differential Equations 15 October 2024 406:302-317
Publikováno v:
Probabilistic Engineering Mechanics 69 (2022) 103289
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical framework adm
Externí odkaz:
http://arxiv.org/abs/2111.07767
The paper addresses one-dimensional transport in a Goupillaud medium (a layered medium in which the layer thickness is proportional to the propagation speed), as a prototypical case of wave propagation in random media. Suitable stochastic assumptions
Externí odkaz:
http://arxiv.org/abs/2103.04729
Publikováno v:
Journal of Sound and Vibration 513(2021), 116409
This paper presents a new approach to modelling wave propagation in random, linearly elastic materials, namely by means of Fourier integral operators (FIOs). The FIO representation of the solution to the equations of motion can be used to identify th
Externí odkaz:
http://arxiv.org/abs/2009.09389
Autor:
Oberguggenberger, Michael
Publikováno v:
In: M. Cicognani, D. Del Santo, A. Parmeggiani, M. Reissig (Eds.), Anomalies in Partial Differential Equations, Springer INdAM Series, Cham 2021, pp. 347-367
The behavior of sufficiently regular solutions to semilinear hyperbolic equations has attracted a great deal of attention in the past decades, concerning local/global existence, finite time blow-up, critical exponents, and propagation of singularitie
Externí odkaz:
http://arxiv.org/abs/2002.05081
The paper is devoted to proving an existence and uniqueness result for generalized solutions to semilinear wave equations with a small nonlinearity in space dimensions 1, 2, 3. The setting is the one of Colombeau algebras of generalized functions. It
Externí odkaz:
http://arxiv.org/abs/1909.05705