Nonlocal problems for parabolic inclusions. (English) Zbl 1187.35300
Summary: We investigate a class of parabolic inclusions with a nonlocal condition of integral type. We provide sufficient conditions that guarantee the existence of at least one solution. Our technique is based on Green’s function for linear parabolic partial differential equations and fixed point theorems for multivalued maps.
MSC:
35R70 | PDEs with multivalued right-hand sides |
35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |
35C15 | Integral representations of solutions to PDEs |
35A08 | Fundamental solutions to PDEs |