- AMS :: Bulletin of the American Mathematical Society
- The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth
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Feireisl, P. Feireisl and F. Convergence for semilinear degenerate parabolic equations in several space dimensions, J. Dynam MR g Feireisl and P. Long-time stabilization of solutions to the Ginzburg-Landau equations of superconductivity MR a An introduction to probability theory and its applications. Real analysis, second ed New York.

Freed and K. Instantons and four-manifolds, second ed. MR 91i Algebraic surfaces and holomorphic vector bundles -Verlag, New York. Friedman and J. Smooth four-manifolds and complex surfaces Berlin. Morgan eds. MR 98j Frigeri, M. Grasselli, and P. Gilbarg and N. Elliptic partial differential equations of second order, second ed New York. Invariance theory, the heat equation, and the Atiyah-Singer index theorem, second ed. MR 98b Grasselli and H. Long-time behavior for a hydrodynamic model on nematic liquid crystal flows with asymptotic stabilizing boundary condition and external force MR SIAM J.

Grasselli, H. Wu, and S. Math Anal. Greene and H. Analytic isometric embeddings, Ann. MR 44 Griffiths and J. MR 80b Grillakis, J. Shatah, and W. Stability theory of solitary waves in the presence of symmetry. I MR 88g Finite time blow-up for the Yang-Mills heat flow in higher dimensions MR e Grotowski and J. Geometric evolution equations in critical dimensions, Calc. Partial MR e Functional calculus of pseudodifferential boundary problems, second ed. MR 96m On elliptic systems in L1 MR 94j The functional calculus for sectorial operators, Operator Theory: Advances and Applications, vol.

Haller-Dintelmann, H. Heck, and M. London Math Soc. MR b Harmonic maps of manifolds with boundary, Lecture Notes in Mathematics, vol. The inverse function theorem of Nash and Moser MR 83j Three-manifolds with positive Ricci curvature MR 84a The formation of singularities in the Ricci flow, Surveys in differential geometry, Vol. Press, Cambridge, MA, , pp. MR 97e Some applications of the Lojasiewicz gradient inequality, Commun. Pure MR Haraux and M. Convergence of solutions of second-order gradient-like systems with analytic nonlinearities, J MR 99a On the convergence of global and bounded solutions of some evolution equations Equ.

The Lojasiewicz gradient inequality in the infinite-dimensional Hilbert space framework MR c Haraux, M. Jendoubi, and O. Rate of decay to equilibrium in some semilinear parabolic equations, J. Evol Equ. Hardy, J. Littlewood, and G. Inequalities, Cambridge University Press, Cambridge,, 2nd ed. Haroske and H. Ordinary differential equations, Classics in Applied Mathematics, vol.

Partial MR Haslhofer and R. Dynamical stability and instability of Ricci-flat metrics MR Heck and M. Heck, M. Hieber, and K. S 3 , Harmonic maps, conservation laws and moving frames, second ed. MR g Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol.

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MR 83j Hewitt and K. Hille and R. MR 54 Hong and L. Global existence for the Seiberg-Witten flow MR b Hong and G. Hong and Y. Anti-self-dual connections and their related flow on 4-manifolds, Calc. Partial MR c The analysis of linear partial differential operators, I.

The analysis of linear partial differential operators, III. Gradient inequalities, Mathematical Surveys and Monographs, vol. Huang and P. Convergence in gradient-like systems which are asymptotically autonomous and analytic MR f Complex geometry, Universitext -Verlag, Berlin,, An introduction.

Elliptic regularization and partial regularity for motion by mean curvature, Mem. MR 95d Bubbling in the harmonic map heat flow, Ph. Pseudo-differential operators and Markov processes, vol.

## AMS :: Bulletin of the American Mathematical Society

Edinburgh Sect. Convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity, J MR 99e A simple unified approach to some convergence theorems of MR 99c MR 93k MR 92h Riemannian geometry and geometric analysis, sixth ed. Perturbation theory for linear operators, second ed New York. Kelleher and J. Singularity formation of the Yang-Mills flow, preprint, February 1,, math. Kleiner and J.

### The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth

Representation theory of semisimple groups, Princeton Mathematical Series, vol. Differential geometry of complex vector bundles, Publications of the Mathematical Society of Japan, vol. MR 89e Kobayashi and K. Foundations of differential geometry. MR 27 MR 38 Kono and T. Weak asymptotical stability of Yang-Mills gradient flow MR 90a Tokyo J.

Regularity problem for quasilinear elliptic and parabolic systems, Lecture Notes in Mathematics, vol.

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Kozono, Y. Maeda, and H. Global solution for the Yang-Mills gradient flow on 4-manifolds MR 97a Nagoya Math. Petun-in, and E. Semenov, Interpolation of linear operators, Translations of Mathematical Monographs, vol. I Translated from the Russian by J. MR 84j Ricci flow, Einstein metrics and the Yamabe invariant. Kronheimer and T. New proof for the existence of locally complete families of complex structures, Proc. Complex Analysis Minneapolis, A.

Aeppli, E. Calabi, and H. Berlin,, pp. MR 31 Asymptotic convergence of harmonic map heat flow, Ph. Smith Translations of Mathematical Monographs, Vol. I MR 39 b. MR 39 Blaine, Jr. Michelsohn, Spin geometry, Princeton Mathematical Series, vol. MR 91g Leng, E. Zhao, and H. Notes on the extension of the mean curvature flow MR Li and X. The gradient flow of Higgs pairs, J. Eur Math. JEMS 13 , Energy identity for the maps from a surface with tension field bounded in Lp MR World Scientific.

Second order parabolic differential equations Publishing Co. Lin and C.

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The analysis of harmonic maps and their heat flows Hackensack, NJ,. Lions and E. Non-homogeneous boundary value problems and applications. MR 50 Liu and X-K. Geometry of Hermitian manifolds Liu and Y. Lockhart and R. Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Pisa Cl. MR 87k MR 28 Ensembles semi-analytiques, , Publ.

Bologna, Bologna, , pp. MR 86m Lorenzi and M. The Kobayashi-Hitchin correspondence Publishing Co. MR 97h MR 96e Lunardi and G. On the domains of elliptic operators in L1, Differential Integral Equations 17 , Energy identity and removable singularities of maps from a Riemann surface with tension field unbounded in L2 MR Lecture notes on mean curvature flow, Progress in Mathematics, vol.

Maugeri, D. Palagachev, and L. Elliptic and parabolic equations with discontinuous coefficients, Mathematical Research, vol. Mawhin and M.

Origin and evolution of the Palais-Smale condition in critical point theory, J. Fixed Point Theory Appl. Sobolev spaces with applications to elliptic partial differential equations, augmented ed. McNamara and Y. An introduction to Banach space theory, Graduate Texts in Mathematics, vol. MR 99k Milgram and P. Harmonic forms and heat conduction. Closed Riemannian manifolds MR 13,a.

Morgan and F. Ricci flow and geometrization of 3-manifolds, University Lecture Series, vol. Morgan and T. The gluing construction for anti-self-dual connections over manifolds with long tubes, preprint, October 13,, pages. Morgan, T. Mrowka, and D. The L2 -moduli space and a vanishing theorem for Donaldson polynomial invariants, Monographs in Geometry and Topology, vol.

MR 95h Morgan and G. A rapidly convergent iteration method and non-linear differential equations. II, Ann. Pisa 3 20 , MR 34 A rapidly convergent iteration method and non-linear partial differential equations. I, Ann. MR 33 Topology: a first course, second ed Englewood Cliffs, N. Shiohama, ed Perspectives in Mathematics, vol. MR 91c Finite time blowing-up for the Yang-Mills gradient flow in higher dimensions MR 95i Hokkaido Math.

Removable singularities for Yang-Mills connections in higher dimensions, J. Fac Sci. London Math. Applied Probability and Queues Applications of Mathematics vol. On an extension of the Kato-Voigt perturbation theorem for substochastic semigroups and its application Taiwanese J. Arlotti L. London Existence of invariant densities for semiflows with jumps J. Boundary conditions in evolutionary equations in biology in: Banasiak J. Mokhtar-Kharroubi M. Amsterdamâ€”New York The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables Proc.

Cambridge Philos. Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models J. B 46 no. Perturbations of positive semigroups in AL-spaces Unpublished manuscript.

Perturbing the boundary conditions of a generator Houston J. Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book, which should be regarded as an extended reference section, presents a survey of the results from functional analysis, the theory of positive operators and the theory of semigroups that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material.

The second part then deals with the application of the developed theory to a variety of problems ranging from the classical birth-and-death type problems of population dynamics, through fragmentation models in both conservative and mass loss regimes, to kinetic models.