STRONGLY GENERALIZED SOLUTION OF A FRACTIONAL PROBLEM OF PARABOLIC EVOLUTION OF ORDER-TWO IN A PLATE WITH INTEGRAL BOUNDARY CONDITIONS

AMETANA Edoh; DJIBIBE MoussaZakari; ALEDA Koulinté

AMETANA Edoh Laboratoire d’Analyse de Modélisation Mathématiques et Applications (LAMMA), Département dc Mathématiques, Université de Lome, PB 1515 Lomé, Togo
DJIBIBE MoussaZakari Laboratoire d’Analyse de Modélisation Mathématiques et Applications (LAMMA), Département dc Mathématiques, Université de Lome, PB 1515 Lomé, Togo
ALEDA Koulinté Laboratoire d’Analyse de Modélisation Mathématiques et Applications (LAMMA), Département dc Mathématiques, Université de Lome, PB 1515 Lomé, Togo

Article ID: 2547

Keywords: fractional equation; non boundary conditions, functional analysis method; non-classical function space; strong solution; energy inequality

Abstract

The aim of this article is to prove uniqueness of solution to mix a fractional problem of parabolic evolution of order-two in a plate with integral boundary conditions: {Dtαv−1x∂∂x(x∂v∂x)−1x2∂2v∂y2=F(x,y,t)v(x,y,0)=φ(x,y)v(ℓ1,y,t)=∂v∂y(x,ℓ2,t)=0∫0ℓ1xv(x,y,t)dx=0∫0ℓ2v(x,y,t)dy=0. A functional analysis method is used. The proof is based on an energy inequality and on a priori estimates established in non-classical function spaces.

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