On a nonuniform parabolic equation with mixed boundary condition

Author:
C. V. Pao

Journal:
Proc. Amer. Math. Soc. **49** (1975), 83-89

MSC:
Primary 35K20

DOI:
https://doi.org/10.1090/S0002-9939-1975-0377286-0

MathSciNet review:
0377286

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Abstract: This paper discusses the existence of weak solutions for an initial boundary-value problem of a nonuniform second order parabolic equation in which the coefficient of is nonnegative and the coefficient matrix of the elliptic part is not necessarily positive definite. When , this problem is reduced to a degenerate elliptic system. A discussion of the existence of weak solutions for the degenerate elliptic boundary-value problem from the parabolic system is included.

**[1]**W. T. Ford,*The first initial boundary-value problem for a nonuniform parabolic equation*, J. Math. Anal. Appl.**40**(1972), 131-137. MR**0320532 (47:9069)****[2]**A. V. Ivanov,*A boundary-value problem for degenerate second order parabolic linear equations*, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)**14**(1969), 48-88. (Russian) MR**0296526 (45:5586)****[3]**J. J. Kohn and L. Nirenberg,*Non-coercive boundary value problems*, Comm. Pure Appl. Math.**18**(1965), 443-492. MR**31**# 6041. MR**0181815 (31:6041)****[4]**R. D. Meyer,*Degenerate elliptic differential systems*, J. Math. Anal. Appl. 29 (1970), 436-442. MR**41**# 2198. MR**0257548 (41:2198)****[5]**M. K. V. Murthy and G. Stampacchia,*Boundary value problems for some degenerate elliptic operators*, Ann. Mat. Pure Appl. (4)**80**(1968), 1-22. MR**40**# 3069. MR**0249828 (40:3069)****[6]**E. T. Poulsen,*Boundary value properties connected with some improper Dirichlet integrals*, Math. Scand.**8**(1960), 5-14. MR**24**# A2140. MR**0132295 (24:A2140)****[7]**D. S. Tartakoff,*On the regularity of non-unique solutions of degenerate elliptic-parabolic systems of partial differential equations*, Comm. Pure Appl. Math.**24**(1971), 763-788. MR**45**# 5543. MR**0296483 (45:5543)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0377286-0

Keywords:
Nonuniform parabolic equations,
degenerate elliptic equations,
weak solutions,
initial boundary-value problems

Article copyright:
© Copyright 1975
American Mathematical Society