Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects

In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first adopt the notion of weak solutions introduced in [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321--359]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques

Complete damage in linear elastic materials - Modeling, weak formulation and existence results

In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential inclusion for the damage process and a quasi-static balance equation for the displacement field which are strongly nonlinearly coupled. In our proposed model, the material may completely disintegrate which is indispensable for a realistic modeling of damage processes in elastic materials. Complete damage theories lead to several mathematical problems since for instance coercivity properties of the free energy are lost and, therefore, several difficulties arise. For the introduced complete damage model, we propose a classical formulation and a corresponding suitable weak formulation in an $SBV$-framework. The main aim is to prove existence of weak solutions for the introduced degenerating model. In addition, we show that the classical differential inclusion can be regained from the notion of weak solutions under certain regularity assumptions which is a novelty in the theory of complete damage models of this type

On the Effects of Redistribution on Growth and Entrepreneurial Risk-Taking

This paper investigates the redistributive effects of taxation on occupational choice and growth. We discuss a twoñsector economy in the spirit of Romer (1990). Agents engage in one of two alternative occupations: either selfñemployment in an intermediate goods sector characterized by monopolistic competition, or employment as an ordinary worker in this sector. Entrepreneurial prots are stochastic. The occupational choice under risk endogenizes the number of rms in the intermediate goods industry. While the presence of entrepreneurial risk results in a suboptimally low number of rms and depresses growth, nonñlinear tax schemes are partly capable of compensating the negative by effects by ex post providing a social insurance.OLG, endogenous growth, entrepreneurship, occupational choice, redistributive taxation

On Entrepreneurial Risk–Taking and the Macroeconomic Effects of Financial Constraints

This paper deals with credit market imperfections and idiosyncratic risks in a two–sector heterogeneous agent dynamic general equilibrium model of occupational choice. We focus especially on the effects of tightening financial constraints on macroeconomic performance, entrepreneurial risk–taking, and social mobility. Contrary to many models in the literature, our comparative static results cover a broad range for borrowing constraints, from an unrestrained to a perfectly constrained economy. In our baseline model, we find substantial gains in output, welfare, and wealth equality associated with credit market improvements. The marginal gains from relaxing constraints are largest for empirically relevant debt–equity ratios. Interestingly, the entrepreneurship rate and social mobility respond non–monotonically to a change in the tightness of financial constraints. The results crucially depend on the degree of income persistence and feedback effects in general equilibrium, where optimal firm sizes and the demand for credit are determined endogenously.CGE, occupational choice, financial constraints, wealth distribution

Endogenous Redistributive Cycles An Overlapping Generations Approach to Social Conflict and Cyclical Growth

This paper discusses the emergence of endogenous redistributive cycles in a stochastic growth model with incomplete asset markets and heterogeneous agents, where agents vote on the degree of progressivity in the tax-transfer-scheme. The model draws from Bénabou (1996) and ties the bias in the distribution of political power to the degree of inequality in the society, thereby triggering redistributive cycles which then give rise to a nonlinear, cyclical pattern of savings rates, growth and inequality over time.Inequality, growth, political cycles, redistribution, Hopf bifurcation

Borrowing Constraints, Entrepreneurial Risks, and the Wealth Distribution in a Heterogeneous Agent Model

This paper deals with credit market imperfections and idiosyncratic risks in a two–sector heterogeneous agent dynamic general equilibrium model of occupational choice. We focus especially on the effects of tightening financial constraints on macroeconomic performance, entrepreneurial risk–taking, and social mobility. Contrary to many models in the literature, our comparative static results cover the entire range of borrowing constraints, from complete markets to a perfectly constrained economy. In our baseline model, we find substantial gains in output, welfare, and wealth equality associated with relaxing the constraints, but argue that it might also prove worthwhile to examine the marginal gains from credit market improvements. Interestingly, the amount of entrepreneurial activity and social mobility increases if borrowing constraints become more tight. These results can be attributed to the general equilibrium nature of our approach, where optimal firm sizes and the demand for credit are determined endogenously. The comparative static results on the entrepreneurship rate and social mobility respond sensitively to a change in income persistence.DSGE model, wealth distribution, occupational choice, borrowing constraints

Modeling and analysis of a phase field system for damage and phase separation processes in solids

In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function. The main aim of this paper is to show existence of weak solutions for the introduced model, where, in contrast to existing damage models in the literature, different elastic properties of damaged and undamaged material are regarded. To prove existence of weak solutions for the introduced model, we start with an approximation system. Then, by passing to the limit, existence results of weak solutions for the proposed model are obtained via suitable variational techniques.Comment: Keywords: Cahn-Hilliard system, phase separation, elliptic-parabolic systems, doubly nonlinear differential inclusions, complete damage, existence results, energetic solutions, weak solutions, linear elasticity, rate-dependent system

The Effects of International Financial Integration in a Model with Heterogeneous Firms and Credit Frictions

This paper examines the pattern of international capital flows in a two-sector dynamic general equilibrium heterogeneous agent model with financial frictions and idiosyncratic entrepreneurial risk. Countries differ only with respect to the tightness of constraints on the domestic credit market. The results provide an explanation for the 'Lucas paradox', i.e., the empirical observation of capital flowing from poor to rich countries, where lending countries are characterized by tighter domestic constraints. International integration only indirectly mitigates negative output and welfare effects from financial constraints on domestic credit markets. The effects are triggered by adjustments in the real interest rate to global real return. We observe an accumulation-driven rise in the entrepreneurship rate and positive output effects for countries with relatively tight constraints who generally benefit from financial integration. The macroeconomic effects can be adverse for the capital-importing country which may suffer from a decrease in GNP in the integrated economy. The model is calibrated to match standard macro data, entrepreneurship rates, and Gini coefficients from OECD countries

Existence of weak solutions for a PDE system describing phase separation and damage processes including inertial effects

In this paper, we consider a coupled PDE system describing phase separation and damage phenomena in elastically stressed alloys in the presence of inertial effects. The material is considered on a bounded Lipschitz domain with mixed boundary conditions for the displacement variable. The main aim of this work is to establish existence of weak solutions for the introduced hyperbolic-parabolic system. To this end, we first adopt the notion of weak solutions introduced in [C. Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011), 321-359]. Then we prove existence of weak solutions by means of regularization, time-discretization and different variational techniques