WELL-POSEDNESS RESULTS FOR FRACTIONAL SEMI-LINEAR WAVE EQUATIONS

被引：20

作者：

Djida, Jean-Daniel ^{[1
]}

Fernandez, Arran ^{[2
]}

Area, Ivan ^{[3
]}

机构：

[1] Univ Santiago de Compostela, Dept Analise Matemat, Santiago De Compostela 15782, Spain

[2] Eastern Mediterranean Univ, Dept Math, Via Mersin 10, Famagusta, Northern Cyprus, Turkey

[3] Univ Vigo, Dept Matemat Aplicada 2, EE Aeronaut & Espazo, Orense 32004, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 02期

关键词：

Fractional partial differential equations; fractional semi-linear wave equations; local and global existence of solutions; regularity estimates; EXTENSION PROBLEM; DIFFERENTIAL-EQUATIONS; REGULARITY; INEQUALITIES; EXISTENCE;

D O I：

10.3934/dcdsb.2019255

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work is concerned with well-posedness results for nonlocal semi-linear wave equations involving the fractional Laplacian and fractional derivative operator taken in the sense of Caputo. Representations for solutions, existence of classical solutions, and some L-p-estimates are derived, by considering a quasi-stationary elliptic problem that comes from the realisation of the fractional Laplacian as the Dirichlet-to-Neumann map for a non-uniformly elliptic problem posed on a semi-infinite cylinder. We derive some properties such as existence of global weak solutions of the extended semi-linear integro-differential equations.

引用

页码：569 / 597

页数：29

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