Semigroup formulation of Rothe’s method: application to parabolic problems
نویسنده
چکیده
A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe’s method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.
منابع مشابه
Convergence of Rothe’s Method for Fully Nonlinear Parabolic Equations
Convergence of Rothe’s method for the fully nonlinear parabolic equation ut +F (D 2u,Du, u, x, t) = 0 is considered under some continuity assumptions on F. We show that the Rothe solutions are Lipschitz in time, and they solve the equation in the viscosity sense. As an immediate corollary we get Lipschitz behavior in time of the viscosity solutions of our equation.
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