On Approximation of Solutions of Parabolic Functional Differential Equations in Unbounded Domains

László Simon ()
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László Simon: L. Eőtvős University of Budapest, Department of Applied Analysis

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 439-451 from Springer

Abstract: Abstract We shall consider initial-boundary value problems for the equation $$D_t u(t,x) - \sum\limits_{j = 1}^n {D_j \left[ {f_j (t,x,u(t,x),\nabla u(t,x))} \right]} + f_0 (t,x,u(t,x),\nabla u(t,x)) + h(t,x,\left[ {H(u)} \right](t,x)) = F(t,x),\;(t,x) \in Q_T = (0,T) \times \Omega $$ where Ω⊂Rn is an unbounded domain with sufficiently smooth boundary, H is a linear continuous operator in L P (Q T ), the functions f i , h satisfy the Caratheodory conditions and certain polynomial growth conditions. We shall show that the weak solutions of this problem can be obtained as the limit (as k→∞) similar problems, considered in (0, T) ×Ωk where Ωk⊂Ω are bounded domains with sufficiently smooth boundary, having the property. $$\Omega _k \supset \Omega \cap B_k (B_k = \{ x \in R^n :\left| x \right|

Keywords: Weak Solution; Existence Theorem; Unbounded Domain; Closed Linear Subspace; Maximal Monotone Mapping (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-8035-0_32

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DOI: 10.1007/978-3-0348-8035-0_32

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