A semigroup treatment of a one-dimensional nonlinear parabolic equation

Serizawa, Hisamitsu

doi:10.1090/S0002-9939-1989-0953746-6

A semigroup treatment of a one-dimensional nonlinear parabolic equation
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Proc. Amer. Math. Soc. 106 (1989), 187-192 Request permission

Abstract:

In this paper we study the existence, uniqueness and differentiability of solutions (in a certain generalized sense) for the nonlinear parabolic equation \[ {u_t} = {u_{xx}} - F(u,{u_x})(0 < x < 1,t > 0),\] under the maximal monotone boundary conditions: \[ {( - 1)^i}{u_x}(t,i) \in {\beta _i}(u(t,i)),t > 0,i = 0,1.\]

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