The Cauchy problem for a system of nonlinear heat equations in two space dimensions

DOI10.1142/S1793557115500047zbMath1333.35092MaRDI QIDQ5247070

Amel Chouichi, Sarah Otsmane

Publication date: 22 April 2015

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessnonlinear heat equationMoser-Trudinger inequality

Mathematics Subject Classification ID

Heat equation (35K05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for second-order parabolic systems (35K45) Semilinear parabolic equations (35K58) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• Unnamed Item
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• On the lack of compactness in the 2D critical Sobolev embedding
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Existence and non-existence of global solutions for a semilinear heat equation
• Cauchy problem for semilinear parabolic equations with initial data in \(H_p^s(\mathbb{R}^n)\) spaces
• Nonuniqueness for a critical nonlinear heat equation with any initial data.
• A sharp Trudinger-Moser type inequality for unbounded domains in \(\mathbb R^2\)
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• A nonlinear heat equation with singular initial data
• Well- and ill-posedness issues for energy supercritical waves
• Ill-posedness of \(H^1\)-supercritical waves
• GLOBAL SOLUTION AND BLOWUP OF SEMILINEAR HEAT EQUATION WITH CRITICAL SOBOLEV EXPONENT
• Admissible L_p norms for local existence and for continuation in semilinear parabolic systems are not the same
• Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity
• ENERGY CRITICAL NLS IN TWO SPACE DIMENSIONS
• Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth
• NON-UNIQUENESS FOR A CRITICAL NON-LINEAR HEAT EQUATION
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents

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