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

In: Function Spaces, Differential Operators and Nonlinear Analysis

Author

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  • László Simon

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

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|

Suggested Citation

  • László Simon, 2003. "On Approximation of Solutions of Parabolic Functional Differential Equations in Unbounded Domains," Springer Books, in: Dorothee Haroske & Thomas Runst & Hans-Jürgen Schmeisser (ed.), Function Spaces, Differential Operators and Nonlinear Analysis, pages 439-451, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-8035-0_32
    DOI: 10.1007/978-3-0348-8035-0_32
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