Results 61 to 70 of about 1,078 (81)

Local energy estimate on Kerr black hole backgrounds [PDF]

arXiv, 2008
We study dispersive properties for the wave equation in the Kerr space-time with small angular momentum. The main result of thispaper is to establish uniform energy bounds and local energy decay for such backgrounds.
arxiv  

Small data global regularity for half-wave maps in n = 4 dimensions. [PDF]

Commun Partial Differ Equ, 2021
Kiesenhofer A, Krieger J.
europepmc   +1 more source

Klein-Gordon potential in characteristic coordinates

Demonstratio Mathematica
By the Klein-Gordon potential, we call a convolution-type integral with a kernel, which is the fundamental solution of the Klein-Gordon equation and also a solution of the Cauchy problem to the same equation.
Kal’menov Tynysbek, Suragan Durvudkhan
doaj   +1 more source

The Fourier transform and the wave equation [PDF]

The American Mathematical Monthly Vol. 118, No. 7 (2011), pp. 599-609, 2009
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Fourier transform.
arxiv  

Analysis for Full-Field Photoacoustic Tomography with Variable Sound Speed. [PDF]

SIAM J Imaging Sci, 2022
Nguyen L, Haltmeier M, Kowar R, Do N.
europepmc   +1 more source

Blow-up of waves on singular spacetimes with generic spatial metrics. [PDF]

Lett Math Phys, 2022
Fajman D, Urban L.
europepmc   +1 more source

Mathematical model of the impact of chemotherapy and antiangiogenic therapy on drug resistance in glioma growth

Computational and Mathematical Biophysics
This study presents a mathematical model of glioma growth dynamics with drug resistance, capturing interactions among five cell populations – glial cells, sensitive and resistant glioma cells, endothelial cells, and neurons – alongside chemotherapy and ...
Hanum Latifah, Susyanto Nanang, Ertiningsih Dwi   +2 more
doaj   +1 more source

Existence of maximizers for Sobolev-Strichartz inequalities [PDF]

arXiv, 2011
We prove the existence of maximizers of Sobolev-Strichartz estimates for a general class of propagators, involving relevant examples, as for instance the wave, Dirac and the hyperbolic Schrodinger flows.
arxiv  

Asymptotic Profiles for wave equations with strong damping [PDF]

arXiv, 2014
We consider the Cauchy problem in ${\bf R}^{n}$ for strongly damped wave equations. We derive asymptotic profiles of these solutions with weighted $L^{1,1}({\bf R}^{n})$ data by using a method introduced in [10].
arxiv  

A Sharp Sobolev--Strichartz estimate for the wave equation [PDF]

arXiv, 2014
We calculate the the sharp constant and characterise the extremal initial data in $\dot{H}^{\frac{3}{4}}\times\dot{H}^{-\frac{1}{4}}$ for the $L^4$ Sobolev--Strichartz estimate for the wave equation in four space dimensions.
arxiv