Abstract
In this chapter we analyze the solution spaces of some differential equations. Mainly the local existence of solutions of nonlinear Timoshenko equation and the existence of solutions of sixth order Boussinesq equation are analyzed. The main results of this part are based on the papers [34, 35]. For further details we also cite [36, 37] and the reference therein.
Keywords: Cauchy problem, weak solution, sixth-order Boussinesq equation, Timoshenko Equation, Gronwalls inequality, blow up, contraction mapping, Young inequality, H¨older inequality, Sobolev-Poincar´e inequality.
Related Books
Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application
Advanced Calculus - Fundamentals of Mathematics
Advanced Numerical Methods for Complex Environmental Models: Needs and Availability
An Introduction to Trigonometry and its Applications
Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods
Applied Computational Mathematics in Social Sciences
Calculus: The Logical Extension of Arithmetic
Complex Analyses in Engineering, Science and Technology
Convergence Theorems for Lattice Group-Valued Measures
Differential and Integral Calculus Theory and Cases