Evolution equations with monotone operator and functional non-linearity at the time derivative
Journal Article
·
· Sbornik. Mathematics
- Tula State University, Tula (Russian Federation)
Conditions for the solubility of the so-called doubly non-linear equations Au + {partial_derivative}/{partial_derivative}t Bu = f, u(0)=u{sub 0} are investigated. Here A is a monotone operator induced by a differential expression containing higher-order partial derivatives and B is an operator induced by a monotone function. A theorem on the existence of a solution is proved. The method of monotone operators is used in combination with the method of compact operators. Examples of applications to parabolic differential equations are presented.
- OSTI ID:
- 21202968
- Journal Information:
- Sbornik. Mathematics, Vol. 191, Issue 9; Other Information: DOI: 10.1070/SM2000v191n09ABEH000506; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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