Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
Reads0
Chats0
TLDR
In this paper, the authors study the Cauchy problem for the Landau Hamiltonian wave equation with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity.Abstract:
In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a ‘very weak solution’ adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.read more
Citations
More filters
Journal ArticleDOI
Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed
TL;DR: In this paper, the authors investigated the well-posedness of the Cauchy problem for operators with a discrete non-negative spectrum acting on a Hilbert space and showed that the wave equation with the distributional coefficient has a unique weak solution.
Journal ArticleDOI
Nonharmonic analysis of boundary value problems without WZ condition
TL;DR: In this article, the eigenfunctions of the model operator on which the construction is based do not have zeros, and the applicability of the developed pseudo-differential analysis is extended.
Journal ArticleDOI
On a non-local problem for a multi-term fractional diffusion-wave equation
Michael Ruzhansky,Michael Ruzhansky,Niyaz Tokmagambetov,Niyaz Tokmagambetov,Berikbol T. Torebek,Berikbol T. Torebek +5 more
TL;DR: In this article, a multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal conditions are given.
Journal ArticleDOI
Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters
TL;DR: In this paper, the authors consider an acoustic problem of wave propagation through a discontinuous medium, which is reduced to the dissipative wave equation with distributional dissipation, and show that this problem has a so-called very weak solution.
Journal ArticleDOI
Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups
TL;DR: In this article, the Cauchy problem for the semilinear damped wave equation for the sub-Laplacian on the Heisenberg group was studied and the global in time well-posedness for small data for power like nonlinearities was shown.
References
More filters
Book
Quantum mechanics: Non-relativistic theory,
TL;DR: The basic concepts of quantum mechanics Energy and momentum Schrodinger's equation Angular momentum Perturbation theory Spin The identity of particles The atom The theory of symmetry Polyatomic molecules Motion in a magnetic field Nuclear structure Elastic collisions Mathematical appendices.
Book
Generalized Coherent States and Their Applications
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
Journal ArticleDOI
Diamagnetismus der Metalle
TL;DR: In this article, the authors gezeigt, das schon freie Elektronen in der Quantentheorie, auser dem Spin-Paramagnetismus, einen von den Bahnen herruhrenden, von Null verschiedenen Diamagnetists haben, welcher in der Teilendlichkeit der ElektRONenbahnen im Magnetfeld seinen Ursprung hat.
Journal ArticleDOI
Bemerkung zur Quantelung des harmonischen Oszillators im Magnetfeld
TL;DR: The exakten Werte der Energieniveaus des isotropen ebenen harmonischen Oszillators in einem zu seiner Ebene senkrechten homogenen magnetfeld sind described in this article.