Nonlinear diffusion induced by nonlinear sources

Authors:
D. D. Joseph and E. M. Sparrow

Journal:
Quart. Appl. Math. **28** (1970), 327-342

MSC:
Primary 80.35

DOI:
https://doi.org/10.1090/qam/272272

MathSciNet review:
272272

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References | Similar Articles | Additional Information

**[1]**D. D. Joseph,*Bounds on for positive solutions of*, Quart. Appl. Math.**23**, 349-354 (1966) MR**0194732****[2]**M. Jakob,*Heat transfer*, Vol. 1, Chap. 10, Wiley, New York, 1949**[3]**P. J. Schneider,*Conduction heat transfer*, Chap. 8, Addison-Wesley, Reading, Mass., 1955**[4]**D. D. Joseph,*Non-linear heat generation and stability of the temperature distribution in conducting solids*, Int. J. Heat Mass Transfer**8**, 281-288 (1965)**[5]**P. J. Torvic,*Temperature rise and stresses due to internal heating*, preprint 68-HT-37, Amer. Soc. Mech. Engrs., 1968**[6]**D. Luss and N. R. Amundson,*Uniqueness of the steady state solutions for chemical reaction occurring in a catalyst particle or in a tubular reactor with axial diffusion*, Chem. Engng. Sci.**22**, 253-266 (1967)**[7]**D. Luss,*Sufficient conditions for uniqueness of the steady state solutions in distributed parameter systems*, Chem. Engng. Sci.**23**, 1249-1255 (1968)**[8]**D. Luss,*On the uniqueness of a large distributed parameter system with chemical reaction and heat and mass diffusion*, Chem. Engng. Sci.**24**, 879-883 (1969)**[9]**D. Luss and J. C. M. Lee,*On global stability in distributed parameter systems*, Chem. Engng. Sci.**23**, 1237-1248 (1968)**[10]**I. M. Gel'fand,*Some problems in the theory of quasilinear equations*, Amer. Math. Soc. Transl. (2)**29**, 295-381 (1963), MR**0153960****[11]**H. Fujita,*On the nonlinear equations*and , Bull. Amer. Math. Soc.**75**, 132-135 (1969) MR**0239258****[12]**S. A. Regirer,*The influence of thermal effects on the viscous resistance of a steady uniform flow of liquid*, J. Appl. Math. Mech.**22**, 580-586 (1958) MR**0102289****[13]**S. A. Kaganov,*Establishing laminar flow for an incompressible liquid in a horizontal channel and a curved cylindrical tube with corrections for frictional heat and the temperature dependence of viscosity*, Int. Chem. Engng.**3**, 33-35 (1963)**[14]**R. E. Colwell and K. R. Nickolls,*The screw extruder*, Ind. Engng. Chem.**51**, 841-843 (1959)**[15]**D. D. Joseph,*Variable viscosity effects on the flow and stability of flow in channels and pipes*, Phys. Fluids**7**, 1761-1771 (1964)**[16]**J. Gavis and R. L. Laurence,*Viscous heating in plane and circular flow between moving surfaces*, I and EC Fundamentals**7**, 232-239 (1968)**[17]**J. Gavis and R. L. Laurence,*Viscous heating of a power-law liquid in plane flow*, I and EC Fundamentals**7**, 525-527 (1968)**[18]**W. K. Ergun,*Self-limiting power excursions in large reactors*, Trans. Amer. Nuclear Soc.**8**, 221 (1965)**[19]**D. S. Cohen,*Positive solutions of nonlinear eigenvalue problems: Applications to nonlinear reactor dynamics*, Arch. Rational Mech. Anal.**26**, 305-315 (1967) MR**0216159****[20]**D. S. Cohen, Correction to reference 19, Arch. Rational Mech. Anal.**30**, 401 (1968) MR**0232084****[21]**D. Luss and N. R. Amundson,*Uniqueness of the steady state for an isothermal porous catalyst*, I and EC Fundamentals**6**, 457-459 (1967)**[22]**H. B. Keller and D. S. Cohen,*Some positone problems suggested by nonlinear heat generation*, J. Math. Mech.**16**, 1361-1376 (1967) MR**0213694****[23]**D. S. Cohen,*Positive solutions of a class of nonlinear eigenvalue problems*, J. Math. Mech.**17**, 209-215 (1967) MR**0213695****[24]**H. B. Keller,*Nonexistence and uniqueness of positive solutions of nonlinear eigenvalue problems*, Bull. Amer. Math. Soc.**74**, 887-891 (1968) MR**0229985****[25]**M. M. Vainberg and V. A. Trenogin,*The Lyapunov and Schmidt methods in the theory of non-linear equations and their subsequent development*, Russian Math. Surveys**17**, no. 2, 1-60 (1962) MR**0154113**

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DOI:
https://doi.org/10.1090/qam/272272

Article copyright:
© Copyright 1970
American Mathematical Society