<p style='text-indent:20px;'>We consider a damped Klein-Gordon equation with variable diffusion coefficient. This problem is challenging because of the equation's unbounded nonlinearity. First, we study nonlinearity's continuity properties. Then existence and uniqueness solutions established. The main result solution map on set admissible parameters. Its application to parameter identific...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 23 October 2019Accepted: 08 January 2021Published online: 15 April 2021Keywordsparameter identification, subdiffusion, fully discrete scheme, convergence, error estimate, Tikhonov regularizationAMS Subject Headings35R11, 35R30, 49M25, 65M60Publication DataISSN (print): 03...

OBJECTIVES To evaluate the preliminary results obtained using diffusion-weighted magnetic resonance imaging and the apparent diffusion coefficient for planning computed tomography-guided biopsies of selected mediastinal lesions. METHODS Eight patients with mediastinal lesions suspicious for malignancy were referred for computed tomography-guided biopsy. Diffusion-weighted magnetic resonance i...

Overdamped motion of Brownian particles in tilted piecewise linear periodic potentials is considered. Explicit algebraic expressions for the diffusion coefficient, current, and coherence level of Brownian transport are derived. Their dependencies on temperature, tilting force, and the shape of the potential are analyzed. The necessary and sufficient conditions for the nonmonotonic behavior of t...

The glucocorticoid receptor (GR) is a transcription factor, which interacts with DNA and other cofactors to regulate gene transcription. Binding to other partners in the cell nucleus alters the diffusion properties of GR. Raster image correlation spectroscopy (RICS) was applied to quantitatively characterize the diffusion properties of EGFP labeled human GR (EGFP-hGR) and its mutants in the cel...

Diffusion tensor imaging is a sensitive way to reflect axonal necrosis and degeneration, glial cell regeneration and demyelination following spinal cord injury, and to display microstructure changes in the spinal cord in vivo. Diffusion tensor imaging technology is a sensitive method to diagnose spinal cord injury; fiber tractography visualizes the white matter fibers, and directly displays the...

Magnetic resonance imaging is used to study changing microstructure and molecular motion during dissolution of poly(vinyl alcohol) (PVA) in water. One-dimensional water concentration profiles were measured as a function of distance from the polymer-solvent interface. Diffusion-weighted profiles were used to calculate the spatial variation of the self-diffusion coefficient of water. The results ...

The relationship between the apparent diffusion coefficient of tissue water measured by MR methods and the physiological status of cells is of particular relevance for better understanding and interpretation of diffusion-weighted MRI. In addition, there is considerable interest in developing diffusion-dependent imaging methods capable of providing novel information on tissue microstructure, inc...