The Cauchy problem for a fourth order parabolic equation by difference methods

Thesis (Ph.D.)--Boston UniversityThis paper deals with the solution of parabolic partial differential equations by difference methods. It is first concerned with obtaining certain basic results for the nth order equation... This enables one to exhibit a stable difference equation compatible with (5). Once assured of the existence of such an equation, it is employed in proving an existence theorem for a solution of the differential equation. The theorem states that if the coefficients a;(x,t) and the function d(x, t) in (5), and the function f(x) in:(2) possess a sufficient number of uniformly continuous and bounded derivatives in R, and a0(x,t) is negative and bounded away from zero, then there exists a solution of (5), (2) possessing a certain number of uniformly continuous and bounded derivatives. [TRUNCATED

Boundedness of Solutions to Differential Equations of Fourth Order with Oscillatory Restoring and Forcing Terms

This paper deals with the boundedness of solutions to a nonlinear differential equation of fourth order. Using the Cauchy formula for the particular solution of nonhomogeneous differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded

Reference list for stability theory in ordinary differential equations

Reference list for stability and control theory in ordinary differential equation