On the analytic theory of Pseudoparabolic systemsFootnote

‡In memory of Professor Stefan Bergman, one of the founders of modern function theoretic methods in partial differential equations.

References

• Behnke , H. and Sommer , F. Theorie der analytischen Funktionen einer komplexen Veränderlichen , Newark/Del : Delaware . Springer-Verlag,Berlin Heidelberg ,1962
   Google Scholar
• Bergman , S. 1969 . Integral Operators in the Theory of Linear Partial Differential Equations , Springer-Verlag New York, Inc. .
   Google Scholar
• Brown , P. M. , Gilbert , R. P. and Hsiao , G. C. 1975 . Constructive function theoretic methods for fourth order pseudoparabolic and metaparabolic equations in two space variables. . Rendiconti di Matematica , 8 ( 4 ) : 935 – 951 .
   Google Scholar
• Colton , D. 1972 . Pseudoparabolic equations in one space variable. . J. Diff. Equations , 12 ( 4 ) : 559 – 565 .
   Web of Science ®Google Scholar
• Colton , D. 1972 . On the analytic theory of pseudoparabolic equations. . Quart. J. Math. Oxford , 23 ( 4 ) : 179 – 192 .
   Web of Science ®Google Scholar
• Colton , D. 1973 . Integral operators and the first initial boundary value problem for pseudoparabolic equations with analytic coefficients. . J. Diff. Equations , 13 ( 4 ) : 506 – 522 .
   Web of Science ®Google Scholar
• Colton , D. 1976 . Partial Differential Equations in the Complex Domain , London, , Melbourne : Pitman Publishing .
   Google Scholar
• Dieudonne , J. 1969 . Foundations of Modern Analysis , New York, , London : Academic Press .
   Google Scholar
• Fuks , B. A. 1965 . Special Chapters in the Theory of Analytic Functions of Several Complex Variables , AMS, Providence .
   Google Scholar
• Gajewski , H. and Groger , K. 1975 . Zur Konvergenz eines Iterationsverfahrens für Gleichungen der Form Au' + Lu=f . Math. Nachr. , 69 : 319 – 331 .
   Google Scholar
• Gajewski , H. and Zacharias , K. 1970 . Zur starken Konvergenz des GALERKINverfahrens bei einer Klasse pseudoparabolischer partieller Differentialgleichungen. . Math. Nachr. , 47 : 365 – 376 .
   Google Scholar
• Garabedian , P. R. 1964 . Partial Differential Equations , London, Sydney : John Wiley .
   Google Scholar
• Gilbert , R. P. Constructive Methods for Elliptic Equations. , Heidelberg, New York : Springer-Verlag, Berlin . Lecture Notes in Mathematics Nr. 365
   Google Scholar
• Gilbert , R. P. and Hsiao , G. C. “ Constructive function theoretic methods for higher order pseudoparaboUc equations. “Function Theoretic Methods for Partial Differential Equations” . Heidelberg, New York : Springer-Verlag, Berlin . Darmstadt 1976, Lecture Notes in Mathem. Nr. 561
   Google Scholar
• Gilbert , R. P. and Roach , G. F. Constructive Methods for Meta and Pseudoparabolic Systems , Delaware, Newark/Del : Inst. Math. Sc. Univ. .
   Google Scholar
• Gilbert , R. P. and Schneider , M. Generalized Meta- und Pseudo-Parabolic Equations in the Plane , Delaware, Newark/Del : Inst. Math. Sc, Univ. .
   Google Scholar
• Grabmiiller , H. 1975 . Relativ akkretive Operatoren und Approximation von Evolutionsgleichungen 2. Art. I. . Math. Nachr. , 66 : 67 – 87 .
   Google Scholar
• Grabmüller , H. 1975 . Relativ akkretive Operatoren und Approximation von Evolutionsgleichungen 2. Art. II. . Math. Nach. , 66 : 89 – 100 .
   Google Scholar
• Haack , W. and Lewy , H. 1959 . On the reflection laws of second order differential equations in two independent variables . Bull. AMS , 65 : 37 – 58 .
   Google Scholar
• Muschelischwili , N. I. 1969 . Singuläre Integralgleichungen , Stuttgart : Birkhäuser, Basel . Akademie-Verlag Berlin 1965
   Google Scholar
• Showalter , R. E. 1968 . “ Pseudo-parabolic differential equations. Doctoral thesis ” . Illinois : Urbana, Univ. .
   Google Scholar
• Showalter , R. E. 1969 . Partial differential equations of Sobolev-Galpern type. . Pacific J. Math , 31 : 787 – 794 .
   Google Scholar
• Showalter , R. E. 1970 . Local regularity of solutions of Sobolev-Galpern partial differential . Pacific J. Math. , 34 : 781 – 787 .
   Google Scholar
• Showalter , R. E. 1970 . Well-posed problems for partial differential equations of order . 2m + l SIAM J. Math. Anal. , 1 : 214 – 231 .
   Google Scholar
• Showalter , R. E. and Ting , T. W. 1970 . Pseudoparabolic partial differential equations . SIAM J.Math. Anal. , 1 : 1 – 26 .
   Google Scholar
• Ting , T. W. 1963 . Certain non-steady flows of second order fluids. . Arch. Rat. Mech. Anal. , 14 : 1 – 26 .
   Web of Science ®Google Scholar
• Ting , T. W. 1969 . Parabolic and pseudoparabolic partial differential equations. . J. Math. Soc.Japan , 21 : 440 – 453 .
   Web of Science ®Google Scholar
• Vekua , I. N. 1963 . Verallgemeinerte analytische Funktionen , Berlin : Akademie-Verlag .
   Google Scholar
• Vekua , I. N. and Wendland , W. 1968 . Elliptic Systems in the Plane , Amsterdam : North-Holland . Pitman Publishing,London, Melbourne 1978
   Google Scholar
• Yu , C. L. 1972 . Reflection principle for systems of first order elliptic equations with analytic coefficients. . Trans. AMS , 164 : 489 – 501 .
   Google Scholar
• Yu , C. L. 1973 . Cauchy problem and analytic continuation for systems of first order elliptic equations with analytic coefficients. . Trans. AMS , 185 : 429 – 443 .
   Google Scholar