Nonlocal problems for a class of nonlinear dissipative Sobolev-type equations

Journal Article · Fri Nov 10 00:00:00 EST 1995 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/BF02367235· OSTI ID:191995

Kotsiolis, A A; Oskolkov, A P; Shadieve, R D

Let H{sub i}, i=0,1,2,3, be Hilbert spaces forming a sequence of compact imedddings. Consider the nonlinear equation in H{sub 2} and suppose that conditions (8)-(12) and (15) hold for the operators A and K (u) and the external force F(t). In the paper, the following two nonlocal problems are studied for Eq. (7) with conditions (8)-(12): (1) Existence in the large of a solution for the Cauchy problem on the semiaxis R{sup +} under various assumptions on F(t). (2) Existence in the large of a solution {omega}-periodic in t, provided that the external force F(t) is {omega}-periodic in t.

• Sponsoring Organization: USDOE
• OSTI ID: 191995
• Journal Information: Journal of Mathematical Sciences, Vol. 77, Issue 2; Other Information: PBD: 10 Nov 1995; TN: Translated from Zapiski Nauchnykh Seminarov POMI; 199, 91-113(1992)
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES
99 MATHEMATICS
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INFORMATION SCIENCE
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NAVIER-STOKES EQUATIONS
NONLINEAR PROBLEMS
INCOMPRESSIBLE FLOW
HILBERT SPACE
BOUNDARY-VALUE PROBLEMS
EQUATIONS OF MOTION