On uniform well-posedness of the abstract Cauchy problem

Remarks on the Well-Posedness of the Nonlinear Cauchy Problem

We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard’s instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems.

Inhomogeneous Two-Parameter Abstract Cauchy Problem

On well-posedness of the Cauchy problem for MHD system in Besov spaces

This paper studies the global well-posedness of solutions to the Cauchy problem of incompressible magneto-hydrodynamics system for large initial data in homogeneous Besov space Ḃ 2 p −1 p,r (R) for 2 < p < ∞ and 1 ≤ r < ∞. In the case of spatial dimension n ≥ 3 we establish the global well-posedness of solution for small data and the local one for large data in Besov space Ḃ n p −1 p,r (R), 1 ≤...

the impact of using inspirational quotes on abstract vocabulary recall

the present study is an attempt to investigate the potential impact of inspirational quotes on improving english abstract vocabulary recall. to achieve this goal, a multiple choice language proficiency test of 60 items including vocabulary and grammar component was administered to a sample of 63 second-semester male and female students whose age ranged between 17 to 22 and they were studying en...

Well-posedness of the Cauchy problem for the fractional power dissipative equations

This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation ut + (−△) u = F (u) for initial data in the Lebesgue space L(R) with r ≥ rd , nb/(2α− d) or the homogeneous Besov space Ḃ p,∞(R ) with σ = (2α − d)/b − n/p and 1 ≤ p ≤ ∞, where α > 0, F (u) = f(u) or Q(D)f(u) with Q(D) being a homogeneous pseudo-differential operator of order d ∈ [0, 2α) and f(u) is a ...