Partial Differential Equations Theory: Sobolev Space, Weak Solution, Semigroup Theory, Fourier and Galerkin Methods

Most modern textbooks on partial differential equations either contain proofs of fundamental results only in special cases, or proof outlines, or do not contain proofs at all. This textbook, despite its relatively small volume, provides all the main results with complete proofs.

The foundation for the material in the textbook is the functional approach associated with the concept of a weak solution and Sobolev spaces. In this textbook, such an approach is demonstrated on second-order model ...