Global existence of solutions to some semilinear integro-differential evolution equations with sign-varying kernels

In this paper, we study the global existence of solutions to some semilinear integro-differential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through fixed point theory and energy method, we obtain the global existence theorem on [0, +∞) of mild and strong solution to the evolution equations with memory effects for oscillating and sign-varying kernels. This theorem generalizes and improves some previous existence results.

GLOBAL REGULAR SOLUTION FOR THE EINSTEIN-MAXWELL-BOLTZMANN-SCALAR FIELD SYSTEM IN A BIANCHI TYPE-I SPACE-TIME

We prove an existence and uniqueness of regular solution to the Einstein-Maxwell-Boltzmann-Scalar Field system with pseudo-tensor of pressure and the cosmological constant globaly in time. We clarify the choice of the function spaces and we establish step by step all the essential energy estimations leading to the global existence theorem.

LAGRANGIAN SYSTEMS WITH NON-SMOOTH CONSTRAINTS

The Lagrange-d'Alembert equations with constraints belonging to H1,∞ have been considered. A concept of weak solutions to these equations has been built. A global existence theorem for Cauchy problem has been obtained.

On the Fourier-Transformed Boltzmann Equation with Brownian Motion

We establish a global existence theorem, and uniqueness and stability of solutions of the Cauchy problem for the Fourier-transformed Fokker-Planck-Boltzmann equation with singular Maxwellian kernel, which may be viewed as a kinetic model for the stochastic time-evolution of characteristic functions governed by Brownian motion and collision dynamics.

The Maxwell-Boltzmann-Euler System with a Massive Scalar Field in All Bianchi Spacetimes

We prove the existence and uniqueness of regular solution to the coupled Maxwell-Boltzmann-Euler system, which governs the collisional evolution of a kind of fast moving, massive, and charged particles, globally in time, in a Bianchi of types I to VIII spacetimes. We clearly define function spaces, and we establish all the essential energy inequalities leading to the global existence theorem.

On Global Existence Theorem of Certain Volterra Integral Equation of Second Kind

The aim of the paper was to fabricate an alternative proof of a global existence theorem of certain type of Volterrea integral equation on the basis of the hypothesis. The new proof has been given by constructing suitable function space and using fixed point theorem. Relaxing some hypotheses in the same and using Bielecki’s notion of norm another global existence theorem has been proposed and proved. DOI: http://dx.doi.org/10.3329/jbas.v36i2.12956 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 2, 147-152, 2012