Qualitative study of some viscoelastic evolution problems

Abstract

n this thesis, we consider the cauchy problem for weakly coupled systems of fractional semilinear Volterra integro di�erential equations of pseudo-parabolic type with a memory term in multi-dimensional space Rn (n � 1), under small initial data and the conditions on the convolution kernel k which are weaker than the classical di�erential inequalities, we establish new results for exponential decay of solutions for single equation of the systems in the Fourier space, and we prove the global existence and uniqueness of solutions for weakly coupled systems where data are supposed to belong to di�erent classes of regularity by introducing a set of time-weighted Sobolev spaces and applying the contracting mapping theorem.