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Applicable Analysis
An International Journal
Volume 85, 2006 - Issue 1-3: In Memory of Carlo Pucci. Guest Editors: Rolando Magnanini and Giorgio Talenti
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Original Articles

On a class of nonlinear nonclassical parabolic equations

J. R. Cannon Department of Mathematics, University of Central Florida, Orlando, FL 32816, USACorrespondence[email protected]
&
M. Salman Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
Pages 23-44 | Received 12 Sep 2003, Accepted 18 Aug 2004, Published online: 25 Jan 2007

References

  • Cannon , JR and Yin , HM . 1989 . A class of non-linear non-classical parabolic equations . Journal of Differential Equations , 79 : 266 – 288 .
  • Evans , LC . 1977 . 1978, A free boundary problem: The flow of two immiscible fluids in a one-dimensional porous medium I . Indiana University Mathematics Journal , 26 : 915 – 931 . II 27, 93–111
  • Ladyzhenskaya , OA , Solonnikov , VA and Ural'ceva , NN . 1968 . Linear and Quaslinear Equations of Parabolic Type , Providence, RI : American Mathematical Society Translations .
  • Cannon , JR and Zachman , D . 1982 . Parameter determination in parabolic partial differential equations from overspecified boundary data . International Journal of Engineering Science , 20 : 779 – 788 .
  • Prilepko , AI and Orlovskii , DG . 1985 . Determination of the evolution parameter of an equation and inverse problems of mathematical physics I . Differentsial'naya Utravneniya , 21 : 119 – 129 . II 21, 694–701
  • Rubenstein , LI . 1971 . The Stefan Problem , Vol. 27 , Providence, RI : American Mathematical Society Translations .
  • Baiocchi , C , Evans , LC , Frank , L and Friedman , A . 1980 . Uniqueness for two immiscible fluid flows in a one-dimensional porous medium . Journal of Differential Equations , 36 : 256 – 294 .
  • Cannon , JR . 1963 . Determination of an unknown coefficient in a parabolic differential equation . Duke Mathematical Journal , 30 : 313 – 323 .
  • Cannon , JR . 1964 . Determination of certain parameters in heat conduction problems . Journal of Mathematical Analysis and Applications , 8 : 188 – 201 .
  • Cannon , JR . 1984 . “ The one-dimensional heat equation ” . In Encyclopedia of Mathematics and its Applications , Vol. 23 , New York : Addison-Wesley .
  • Cannon , JR and DuChateau , PC . 1980 . An inverse problem for a nonlinear diffusion equation . SIAM Journal on Applied Mathematics , 39 : 273 – 289 .
  • Cannon , JR and Yin , HM . 1988 . A uniqueness theorem for a class of nonlinear parabolic inverse problems . Inverse Problems , 4 : 411 – 416 .
  • Cannon , JR , Yanping , Lin and Shingmin , Wang . 1992 . Determination of source parameter in parabolic equations . Meccanica , 27 : 85 – 94 .
  • Jim Douglas Jr and Frank Jones , B . 1962 . The determination of a coefficient in a parabolic differential equation, Part II Numerical approaximation . Journal of Mathematics and Mechanics , 11 : 919 – 926 .
  • Friedman , A . 1964 . Partial Differential Equations of Parabolic Type , Englewood Cliffs, NJ : Prentice-Hall .
  • Friedman , A . 1976 . Analyticity of the free boundary for the Stefan problem . Archive for Rational Mechanics and Analysis , 61 : 97 – 125 .
  • Kruzkov , SN . 1967 . Nonlinear parabolic equations in two independent variables . Transactions of the Moscow Mathematical Society , 16 : 355 – 373 .

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