Dedicated to Academician Professor Gradimir Milovanović on the occasion of his 70th birthday. Miles Caddick and Endre SüliT his paper is concerned with the proof of existence and numerical approximation of large-data global-in-time Young measure solutions to initial-boundaryvalue problems for multidimensional nonlinear parabolic systems of forwardbackward type of the form Btu´divpapDuqq`Bu " F , where B P R mˆm , Bv¨v ě 0 for all v P R m , F is an m-component vector-function defined on a bounded open Lipschitz domain Ω Ă R n , and a is a locally Lipschitz mapping of the form apAq " KpAqA, where K : R mˆn Ñ R. The function a may have unequal lower and upper growth rates; it is not assumed to be monotone, nor is it assumed to be the gradient of a potential. We construct a numerical method for the approximate solution of problems in this class, and we prove its convergence to a Young measure solution of the system.
This paper is concerned with the proof of existence and numerical approximation of large-data globalin-time Young measure solutions to initial-boundary-value problems for multidimensional nonlinear parabolic systems of forward-backward type of the form ∂tu − div(a(Du)) + Bu = F , whereand a is a locally Lipschitz mapping of the form a(A) = K(A)A, where K : R m×n → R. The function a may have a nonstandard growth rate, in the sense that it is permitted to have unequal lower and upper growth rates. Furthermore, a is not assumed to be monotone, nor is it assumed to be the gradient of a potential. Problems of this type arise in mathematical models of the atmospheric boundary layer and fall beyond the scope of monotone operator theory. We develop a numerical algorithm for the approximate solution of problems in this class, and we prove the convergence of the algorithm to a Young measure solution of the system under consideration.Dedicated to Academician Professor Gradimir Milovanović on the occasion of his 70th birthday.
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