On B-evolution theory and dynamic boundary conditions on a portion of the boundary

References

• Barenblatt , g. , Zheltov , i and Kochiva , i . 1960 . Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks . J. Appl. Math. Mech , 24 : 1286 – 1303 .
   Google Scholar
• Brill , H. 1977 . A semilinear Sobolev equation in a Banach space . J. Differential Equations , 24 : 412 – 425 .
   Web of Science ®Google Scholar
• Cannon , J. and Meyer , G . 1971 . On diffusion in a fractured medium . SI AM J. App. Math , 20 : 434 – 438 .
   Google Scholar
• Carroll , R.V. and Showalter , R.E . 1976 . Singular and degenerate Cauchy problems , New York : Academic Press .
   Google Scholar
• Greybe , V.G. 1984 . Steuringteorie vir evolusievergelykings , Pretoria Univ .
   Google Scholar
• Grobbelaar-Van Dalsen , M. 1985 . An evolution problem involving non-stationary operators between two Banach spaces I-II . juaestiones Math , 8 : 97 – 130 .
   Google Scholar
• Grobbelaar-Van Dalsen , M. 1986 . “ Fractional powers of a closed pair of operators ” . In Proc. Roy. Soc. Edinburgh Sect , Vol. 102 , 149 – 158 . Zurich Universitat .
   Google Scholar
• Grobbelaar-Van Dalsen , M. 1987 . “ Semilinear evolution equations and fractional powers of a closed pair of operators ” . In Proc. Roy. Soc. Edinburgh Sect , Vol. 105 , 101 – 115 . Zurich Universitat .
   Google Scholar
• Sauer , N. 1989 . Dynamic boundary conditions for the Navier-Stokes equations . Proc. Roy. Soc. Edinburgh Sect , 113 : 1 – 11 .
   Google Scholar
• Hintermann , T. 1988 . Evolutionsgleichungen mit dynamischen randbe-dingungen , Zurich Universitat .
   Google Scholar
• Janse van Rensburg , N.F. 1982 . Dinamiese randvoorwaardes vir parsiele differensiaalvergelykings , Pretora Univ .
   Google Scholar
• Langer , R.E. 1932 . A problem in diffusion or in the flow of heat for a solid in contact with a fluid . Tohoku Math. Journal , 35 : 260 – 275 .
   Google Scholar
• Lions , J.L. 1961 . Equations differentielles operationelles et problemes aux limites , Berlin : Springer-Verlag .
   Google Scholar
• Lions , J.L. and Magenes , E . 1972 . Non-homogeneous boundary-value problems and applications , Berlin : Springer-Verlag .
   Google Scholar
• Milne , E.A. 1926 . The diffusion of imprisoned radiation through a gas . J. London Math. Soc , 1 : 40 – 51 .
   Google Scholar
• Sauer , N. 1982 . Linear evolution equations in two Banach spaces . Proc. Roy. Soc. Edinburgh Sect , 91 : 287 – 303 .
   Google Scholar
• Sauer , N. 1980 . Linear evolution equations in two Banach spaces . Pretoria Univ. Dept. kppl. Math. Research Report , 17
   Google Scholar
• Schechter , M. 1960 . Various types of boundary conditions for elliptic equations . Comm. Pure kppl. Math , 13 : 407 – 425 .
   Google Scholar
• Showalter , R.E. 1974 . Degenerate evolution equations and applications . Indiana Univ. Math. Jour , 23 : 655 – 677 .
   Web of Science ®Google Scholar
• Tanabe , H. 1979 . Equations of evolution , London : Pitman .
   Google Scholar
• Taylor , D.V. 1942 . Research on consolidation of days , Cambridge : Massachusetts Institute of Technology Press .
   Google Scholar
• Ting , T.V. 1963 . Certain non-steady flows of second-order fluids . Arch. Rational Mech. Anal , 14 : 1 – 26 .
   Web of Science ®Google Scholar
• van Dalsen , M. Die teorie van nie-stasionere evolusies geasso-sieer met dinamies-gekoppelde randwaardeprobi erne , 1978 Pretoria Univ .
   Google Scholar
• Yagi , A. 1976 . On the abstract linear evolution equations in Banach spaces . J. Math. Soc. Japan , 28 : 290 – 303 .
   Google Scholar
• Yagi , A. 1977 . On the abstract evolution equation of parabolic type . Osaka J. Math , 14 : 557 – 568 .
   Google Scholar
• Yosida , K. 1965 . Functional Analysis , Berlin : Springer-Verlag .
   Google Scholar