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Implicit parabolic differential equations

Published online by Cambridge University Press:  17 April 2009

Salvatore Bonafede  and
Salvatore A. Marano
Salvatore Bonafede
Affiliation:
Dipartimento di Matematica, Universita' di Catania, Viale A. Doria 6 – 95125 Catania, Italy
Salvatore A. Marano
Affiliation:
Dipartimento di Matematica, Universita' di Catania, Viale A. Doria 6 – 95125 Catania, Italy
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Abstract

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Let QT = ω x (0, T), where ω is a bounded domain in ℝn (n ≥ 3) having the cone property and T is a positive real number; let Y be a nonempty, closed connected and locally connected subset of ℝh; let f be a real-valued function defined in QT × ℝh × ℝnh × Y; let ℒ be a linear, second order, parabolic operator. In this paper we establish the existence of strong solutions (n + 2 ≤ p < + ∞) to the implicit parabolic differential equation

with the homogeneus Cauchy-Dirichlet conditions where u = (u1, u2, …, uh), Dxu = (Dxu1, Dxu2, …, Dxuh), Lu = (ℒu1, ℒu2, … ℒuh).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 501 - 509
Copyright
Copyright © Australian Mathematical Society 1995

References

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