On the solutions of nonlinear initial-boundary value problems. (English) Zbl 1103.35337

Ďurikovič, Vladimír; Ďurikovičová, Monika

Siafarikas, Panayiotis D. (ed.), International conference on differential, difference equations and their applications, July 1–5, 2002, Patras, Greece. Cairo: Hindawi Publishing Corporation (ISBN 977-5945-14-3/hbk). 153-170 (2004).

Summary: We deal with the general initial-boundary value problem for a second-order nonlinear nonstationary evolution equation. The associated operator equation is studied by the Fredholm and Nemitskii operator theory. Under local Hölder conditions for the nonlinear member, we observe quantitative and qualitative properties of the set of solutions of the given problem. These results can be applied to different mechanical and natural science models.
For the entire collection see [Zbl 1089.34002].

MSC:

35K60	Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K20	Initial-boundary value problems for second-order parabolic equations
47F05	General theory of partial differential operators
47A53	(Semi-) Fredholm operators; index theories
47H30	Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)

Keywords:

local Hölder conditions