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Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures

In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1–204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of ...

Infimal Convolution Regularisation Functionals of BV and \(\varvec{\mathrm {L}}^{\varvec{p}}\) Spaces

We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation seminorm and \(\mathrm {L}^{p}\) norms. A unified well-posedness analysis is presented and a detailed study of the one-dimensional model is performed, by computing exact solutions for the ...

Partial differential equation models in the socio-economic sciences

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In ...

Changes in Soil Carbon and Enzyme Activity As a Result of Different Long-Term Fertilization Regimes in a Greenhouse Field

In order to discover the advantages and disadvantages of different fertilization regimes and identify the best management practice of fertilization in greenhouse fields, soil enzyme activities involved in carbon (C) transformations, soil chemical characteristics, and crop yields were monitored after long-term (20-year) fertilization regimes, including no fertilizer (CK), 300 kg N ...

Frozen Cropland Soil in Northeast China as Source of N2O and CO2 Emissions

Agricultural soils are important sources of atmospheric N2O and CO2. However, in boreal agro-ecosystems the contribution of the winter season to annual emissions of these gases has rarely been determined. In this study, soil N2O and CO2 fluxes were measured for 6 years in a corn-soybean-wheat rotation in northeast China to quantify the contribution of wintertime N2O and CO2 fluxes ...

A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration

In this paper, we propose a unified primal-dual algorithm framework for two classes of problems that arise from various signal and image processing applications. We also show the connections to existing methods, in particular Bregman iteration (Osher et al., Multiscale Model. Simul. 4(2):460–489, 2005) based methods, such as linearized Bregman (Osher et al., Commun. Math. Sci. ...