Analytic Fragmentation Semigroups and Classical Solutions to Coagulation–fragmentation Equations — a Survey

Integrodifferential Equations with Analytic Semigroups

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

Analytic Structure of Solutions to Multiconfiguration Equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree–Fock) of Coulomb systems. We prove the following: Let {φ1, . . . , φM} be any solution to the rank–M multiconfiguration equations for a molecule with L fixed nuclei at R1, . . . , RL ∈ R. Then, for any j ∈ {1, . . . , M}, k ∈ {1, . . . , L}, there exi...

Analytic solutions of hydrodynamics equations

Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is poss...

Asymptotic Behaviour of Solutions to the Coagulation - Fragmentation Equations

Existence and Uniqueness of Density Conserving Solutions to the Coagulation-Fragmentation Equations With Strong Fragmentation