Hyperbolic-parabolic singular perturbations for scalar nonlinearities

References

• Bazley , N. W. and Kiipper , T. 1981 . Bifurcation Diagrams and Periodic Solutions to Nonlinear Equations . ZAMP , 32 : 470 – 473 .
   Web of Science ®Google Scholar
• Bazley , N.W. and Weinacht , R.J. 1983 . A Class of Operator Equations in Nonlinear Mechanics . Applicable Analysis , 15 : 7 – 14 .
   Web of Science ®Google Scholar
• Bazley , N.W. and Weinacht , R.J. 1985 . A Class of Explicitly Resolvable Evolution Equations . Math. Meth. in the Appl. Sci. , 7 : 426 – 431 .
   Google Scholar
• Briill , L. 1983 . Zur Existenztheorie von nichtlinearen Schrodinger-und Wei- lengleichungen ohne Lipschitz-Voraussetzungen . Nonlinear Analysis , 7 : 1193 – 1208 .
   Web of Science ®Google Scholar
• Courant , R. and Hilbert , D. 1962 . Methods of Mathematical Physics , New York : Interscience Publishers .
   Google Scholar
• Dafermos , C.M. and Nohel , J.A. 1979 . Energy Methods for Nonlinear Hyperbolic Volterra Integrodifferential Equations . Comm. in Partial Differential Equations , 4 : 219 – 278 .
   Google Scholar
• de Brito , E.H. 1982 . The Damped Elastic Stretched String Equation Gen- eralized: Existence, Uniqueness, Regularity and Stability . Applicable Analysis , 13 : 219 – 233 .
   Web of Science ®Google Scholar
• de Jager , E.M. 1975 . Singular Perturbations of Hyperbolic Type . Nieuw. Arch. Wish. , 23 : 145 – 171 .
   Google Scholar
• de Jager , E.M. and Geel , R. 1981 . Singular Perturbations of Hyperbolic Type . Analytical and Numerical Approaches to Asymptotic Problems in Analysis , 47 : 57 – 71 .
   Google Scholar
• Dickey , R.W. 1980 . Stability of Periodic Solutions of the Nonlinear String . Quart of Appl. Math , 38 : 253 – 259 .
   Web of Science ®Google Scholar
• Esham, Jr , B.F. 1982 . A Singularly Perturbed Cauchy Problem for an Evolution Equation in Hilbert Space, Diss , University of Delaware .
   Google Scholar
• Esham, Jr , B.F. 1987 . Asymptotics and an asymptotic Galerkin method for hyperbolic-parabolic singular perturbation problems . SIAM J. Math. Anal. , 18 : 762 – 776 .
   Google Scholar
• Fattorini , H.O. 1983 . The Cauchy Problem . Encyclopedia of Mathematics and its Applications , 18
   Google Scholar
• Fattorini , H.O. 1983 . Singular perturbation and boundary layer for an abstract Cauchy problem . Jour. Math. Anal. Appl. , 97 : 529 – 571 .
   Web of Science ®Google Scholar
• Fattorini , H.O. 1985 . Second Order Linear Differential Equations in Banach Spaces . North Holland Math. Studies , 108
   Google Scholar
• Gael , R. 1981 . Nonlinear initial value problems with singular perturbation of hyperbolic type . Proc, Roy, Soc. , A 89 : 333 – 345 .
   Google Scholar
• Genet , J. and Madaune , M. 1978 . Singular perturbations for a class of nonlinear hyperbolic-hyperbolic problems . J, Math, Anal, Appl. , 84 : 1 – 24 .
   Web of Science ®Google Scholar
• Greenberg , J.M. and Hu , S.C. 1980 . The initial-value problem for a stretched string . Quart, of AppL Math , 38 : 289 – 311 .
   Web of Science ®Google Scholar
• Heinz , E. , W. von , Wahl and einem , Satz von F. E. 1975 . Browder iiber nichtlineare Wellengleichungen . Math, Z. , 141 : 33 – 45 .
   Web of Science ®Google Scholar
• Hsiao , G.C. and Weinacht , R.J. 1979 . A Singularly Perturbed Gauchy Problem . J. Math. Anal. Appl. , 71 : 242 – 250 .
   Web of Science ®Google Scholar
• Hsiao , G.C. and Weinacht , R.J. 1980 . Singular Perturbations for a Weakly Nonlinear Hyperbolic Equation . AppL Anal. , 10 : 221 – 229 .
   Google Scholar
• Hsiao , G.C. and Weinacht , R.J. 1983 . Singular Perturbations for a Sem-ilinear Hyperbolic Equation . SIAM J, Math, Anal. , 14 : 1168 – 1179 .
   Web of Science ®Google Scholar
• Lange , H. 1984 . Blow-up of solutions to singular nonlinear Schrodlnger equations , Varna : Proc. Tenth Int. Conf. on Nonlinear Oscillations .
   Google Scholar
• Medeiros , L.A. 1979 . On a New Class of Nonlinear Wave Equations . J. Math. Anal Appl. , 69 : 252 – 262 .
   Web of Science ®Google Scholar
• Miletta , P.D. Approximation of Solutions to Evolution Equations
   Google Scholar
• Nayfeh , A.H. and Mook , D.T. 1979 . Nonlinear Oscillations , New York : Wiley- Interscience .
   Google Scholar
• Nishida , T. 1971 . A Note on the Nonlinear Vibrations of the Elastic String . Mem. Fac. Eng , 34 : 329 – 341 .
   Google Scholar
• Rommerskirchen , H. 1982 . Singulare Storungen bei einer speziellen Klasse von Wellengleichungen , Koln : Diss. Univ .
   Google Scholar
• Slemrod , M. 1981 . Global Existence, Uniqueness, and Asymptotic Stability of Classical Smooth Solutions in One-Dimensional Non-Linear Thermoelasticity . Arch. Rational Mech, Anal. , 2 : 97 – 133 .
   Google Scholar
• Tapia , O. and Goscinski , O. 1981 . Self-consistent Reaction Field Theory of Solvent Effects . Molecular Physics , 2 : 1975 – 1653 .
   Google Scholar