1. Adjoints of solution semigroups and identifiability of delay differential equations in Hilbert spacesMiklavž Mastinšek, 1994, original scientific article Abstract: The paper deals with semigroups of operators associated with delay differential equation: ▫$dot{x}=Ax(t)+L_1x(t-h)+L_2x_t$▫, where ▫$A$▫ is the infinitesimal generator of an analytic semigroup on a Hilbert space ▫$X$▫ and ▫$L_1$▫, ▫$L_2$▫ are densely defined closed operators in ▫$X$▫ and ▫$L^2(-h,0;X)$▫ respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigenspaces of the generator of the adjoint semigroup are studied and the identifiability of parameters of the equation is given.
Keywords: matematika, analiza, navadne diferencialne enačbe, polgrupe operatorjev, diferencialne enačbe z zakasnitvijo, polgrupe rešitev, adjungirane polgrupe, prepoznavnost
Published: 10.07.2015; Views: 402; Downloads: 31
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2. Arendt, Wolfgang; Bu, Shangquan: Tools for maximal regularity. - Math. Proc. Camb. Philos. Soc. 134, no. 2, 317-336 (2003). [ISSN 0305-0042; ISSN 1469-8064]Miklavž Mastinšek, 2004, review, book review, critique Keywords: matematika, teorija operatorjev, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, maksimalna regularnost, nehomogeni Cauchyjev problem, mathematics, operator theory, ordinary differential equations, ▫$C_0$▫-semigroups, maximal regularity, inhomogeneous Cauchy problem, UMD-space, mild solution
Published: 10.07.2015; Views: 531; Downloads: 24
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3. Mastinšek, Miklavž: Structural operators for abstract functional differential equations. - Semigroup theory and applications, Proc. Conf. Trieste/Italy, Lect. Notes Pure Appl. Math. 116, 303-314 (1989)Miklavž Mastinšek, 1990, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ulomljene potence operatorjev, strukturni operatorji, mathematics, ordinary differential equations, fractional powers of operators, structural operators, abstract functional differential equations
Published: 10.07.2015; Views: 391; Downloads: 18
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4. Megan, M.; Sasu, A. L.; Sasu, B.; Pogan, A.: Exponential stability and unstability of semigroups of linear operators in Banach spaces. - Math. Inequal. Appl. 5, no. 3, 557-567 (2002). [ISSN 1331-4343]Miklavž Mastinšek, 2004, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, ▫$C_0$▫-polgrupe, stabilnost, mathematics, ordinary differential equations, ▫$C_0$▫-semigroups, uniform exponential stability
Published: 10.07.2015; Views: 440; Downloads: 19
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5. Xu, Rui; Chaplain, M. A. J.; Chen, Lansun: Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays. -Appl. Math. Comput. 130, no. 2-3, 295-309 (2002). [ISSN 0096-3003]Miklavž Mastinšek, 2004, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, Lotka-Volterrov sistem, stabilnost, funkcional Ljapunova, mathematics, ordinary differential equations, Lotka-Volterra system, Lyapunov functional, global asymptotic stability, infinite delays
Published: 10.07.2015; Views: 496; Downloads: 10
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6. Agarwal, Shruti; Bahuguna, Dhirendra: Existence and uniqueness of strong solutions to nonlinear nonlocal functional differential equations. - Electron. J. Differ. Equ. 2004, Paper No. 52, 9 p., electronic only (2004). [ISSN 1072-6691]Miklavž Mastinšek, 2005, review, book review, critique Keywords: matematika, analiza, nelinearne navadne diferencialne enačbe, nelokalni problemi, mathematics, analysis, nonlocal problem, accretive operator, method of lines
Published: 10.07.2015; Views: 364; Downloads: 6
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7. Karunanithi, S.; Anthoni, S.M.: Existence of mild solutions of nonlinear functional integro-differential equations of neutral type. (English). - [CA] Sahadevan, R. (ed.) et al., Nonlinear systems. Proceedings of the 8th Ramanujan symposium on recent developments in nonlinear systems, University of Madras, Chennai, India, February 14-16, 2001. Boca Raton, FL: Chapman and Hall/CRC; New Delhi: Narosa Publishing House. 207-219 (2002). [ISBN 0-8493-1722-3; ISBN 81-7319-456-4]Miklavž Mastinšek, 2005, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, nelinearni funkcional, integro-diferencialna enačba, nevtralni tip, mathematics, ordinary differential equations, nonlinear functional, integro-differential equation, neutral type, mild solution
Published: 10.07.2015; Views: 324; Downloads: 15
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8. Voigt, Jürgen: The modulus semigroup for linear delay equations II. (English). - [J] Note Mat. 25, No. 2, 191-208 (2006).[ISSN 1123-2536; ISSN 1590-0932]Miklavž Mastinšek, 2007, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, teorija operatorjev, funkcijska diferencialna enačba, teorija perturbacij, mathematics, ordinary differential equations, operator theory, functional differential equation, modulus semigroup, perturbation theory
Published: 10.07.2015; Views: 632; Downloads: 9
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9. Balachandran, K.; Ravikumar, R.: Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces. (English). - [J] Tamkang J. Math. 37, No. 3, 193-205 (2006). [ISSN 0049-2930]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, polgrupe nelinearnih operatorjev, mathematics, differential equations, delay integrodifferential equation, nonlocal condition
Published: 10.07.2015; Views: 413; Downloads: 24
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10. Faria, Teresa: Asymptotic stability for delayed logistic type equations. (English). - [J] Math. Comput. Modelling 43, No. 3-4, 433-445 (2006). [ISSN 0895-7177]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, populacijska dinamika, mathematics, differential equations, delayed logistic equation, delayed population model, global asymptotic stability
Published: 10.07.2015; Views: 697; Downloads: 5
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