×

Construction of variational factors for quasilinear second order partial differential equations. (English) Zbl 1008.49028

Summary: Using our method developed previously the following results are delivered. For concrete types of quasi-linear partial differential equations (PDEs) for which the classical variational principle is fulfilled, solutions are constructed in explicit form with some variational factors. It has also been demonstrated the existence of some particular cases where the above mentioned solutions does not exist. For certain linear PDE types such solutions are described. Concerning linear PDEs of hyperbolic and elliptic type, the solution, lead to lower bounded functionals.

MSC:

49N45 Inverse problems in optimal control
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI