Global and blowup solutions of semilinear heat equation involving the square root of the Laplacian

DOI10.1186/s13661-015-0384-7zbMath1381.35233OpenAlexW1750262763WikidataQ59434760 ScholiaQ59434760MaRDI QIDQ284142

Yongqiang Xu, Daoheng Sun, Zhong Tan

Publication date: 17 May 2016

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-015-0384-7

zbMATH Keywords

existenceasymptoticSobolev trace inequalitysquare root of the Laplacian

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Singular nonlinear integral equations (45G05) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58) Fractional partial differential equations (35R11)

Cites Work

• Unnamed Item
• The Brezis-Nirenberg type problem involving the square root of the Laplacian
• The Nehari manifold for elliptic equation involving the square root of the Laplacian
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Decay of mass for nonlinear equation with fractional Laplacian
• Asymptotic stability and blowing up of solutions of some nonlinear equations
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Heat flow for the square root of the negative Laplacian for unit length vectors
• GLOBAL SOLUTION AND BLOWUP OF SEMILINEAR HEAT EQUATION WITH CRITICAL SOBOLEV EXPONENT
• A concave—convex elliptic problem involving the fractional Laplacian
• Global Well-Posedness for the Fractional Nonlinear Schrödinger Equation
• Solutions globales d'equations de la chaleur semi lineaires.
• Regularity of the obstacle problem for a fractional power of the laplace operator
• An Extension Problem Related to the Fractional Laplacian
• Semilinear parabolic equations involving critical Sobolev exponent: Local and asymptotic behavior of solutions
• Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws