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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A semigroup treatment of a one-dimensional nonlinear parabolic equation


Author: Hisamitsu Serizawa
Journal: Proc. Amer. Math. Soc. 106 (1989), 187-192
MSC: Primary 35K55; Secondary 35K15, 47H06, 47H15, 58D07, 58D25
MathSciNet review: 953746
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Abstract: In this paper we study the existence, uniqueness and differentiability of solutions (in a certain generalized sense) for the nonlinear parabolic equation

$\displaystyle {u_t} = {u_{xx}} - F(u,{u_x})(0 < x < 1,t > 0),$

under the maximal monotone boundary conditions:

$\displaystyle {( - 1)^i}{u_x}(t,i) \in {\beta _i}(u(t,i)),t > 0,i = 0,1.$


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0953746-6
PII: S 0002-9939(1989)0953746-6
Keywords: Nonlinear boundary value problem, $ m$-dissipative operator
Article copyright: © Copyright 1989 American Mathematical Society