Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Semilinear evolution equations in Banach spaces with application to parabolic partial differential equations

Author: Samuel M. Rankin
Journal: Trans. Amer. Math. Soc. 336 (1993), 523-535
MSC: Primary 34G20; Secondary 35K55, 47H20
MathSciNet review: 1052911
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A theory for a class of semilinear evolution equations in Banach spaces is developed which when applied to certain parabolic partial differential equations with nonlinear terms in divergence form gives strong solutions even for nondifferentiable data.

References [Enhancements On Off] (What's this?)

  • [1] Lamberto Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova 31 (1961), 308–340 (Italian). MR 0138894
  • [2] Thomas J. Bridges, The Hopf bifurcation with symmetry for the Navier-Stokes equations in (𝐿_{𝑝}(Ω))ⁿ, with application to plane Poiseuille flow, Arch. Rational Mech. Anal. 106 (1989), no. 4, 335–376. MR 997106, 10.1007/BF00281352
  • [3] Avner Friedman, Partial differential equations, Holt, Rinehart and Winston, Inc., New York-Montreal, Que.-London, 1969. MR 0445088
  • [4] Daisuke Fujiwara and Hiroko Morimoto, An 𝐿ᵣ-theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 24 (1977), no. 3, 685–700. MR 0492980
  • [5] Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244
  • [6] Melvin L. Heard and Samuel M. Rankin III, Weak solutions for a class of parabolic Volterra integrodifferential equations, J. Math. Anal. Appl. 139 (1989), no. 1, 78–109. MR 991928, 10.1016/0022-247X(89)90231-X
  • [7] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, vol. 44, Springer-Verlag, New York, 1983. MR 710486
  • [8] Roger Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, vol. 68, Springer-Verlag, New York, 1988. MR 953967
  • [9] Hans Triebel, Interpolation theory, function spaces, differential operators, North-Holland Mathematical Library, vol. 18, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503903
  • [10] Fred B. Weissler, Semilinear evolution equations in Banach spaces, J. Funct. Anal. 32 (1979), no. 3, 277–296. MR 538855, 10.1016/0022-1236(79)90040-5
  • [11] Kôsaku Yosida, Functional analysis, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR 617913

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34G20, 35K55, 47H20

Retrieve articles in all journals with MSC: 34G20, 35K55, 47H20

Additional Information

Keywords: Banach spaces, semigroup of operators, fractional powers of closed unbounded operators
Article copyright: © Copyright 1993 American Mathematical Society