Local well-posedness and ill-posedness on the equation of type □u = uk(partial derivativeu)α

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H-s and H-s for semilinear wave equations with polynomial nonlinearity in u and partial derivative u. This ill-posed result concerns the focusing type equations with nonlinearity on u and partial derivative(t)u.