Premium
Existence of unbounded solutions to parabolic equations with functional dependence
Author(s) -
Bychowska Agnieszka
Publication year - 2004
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310123
Subject(s) - pointwise , mathematics , uniqueness , lipschitz continuity , mathematical analysis , nonlinear system , type (biology) , parabolic partial differential equation , differential equation , physics , ecology , quantum mechanics , biology
The Cauchy problem for nonlinear parabolic differential‐functional equations is considered. Under natural generalized Lipschitz‐type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u ( · ); (ii) the functional dependence u ( · ) and ∂ x u ( · ); (iii) the functional dependence u ( · ) and the pointwise dependence ∂ x u ( t, x ). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)