Subsolutions and super solutions to systems of parabolic equations with applications to generalized Fujita‐type systems

DOI10.1002/mma.1670171302zbMath0807.35061OpenAlexW1971702845MaRDI QIDQ4312287

Sleeman, Brian D., Gang Lu

Publication date: 1 March 1995

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.1670171302

zbMATH Keywords

blow-upFujita-type systemssub- or supersolutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (9)

Supersolutions for a class of nonlinear parabolic systems ⋮ Global existence and blow-up for a class of semilinear parabolic systems: A Cauchy Problem ⋮ Viscosity solutions of fully nonlinear parabolic systems. ⋮ The role of critical exponents in blow-up theorems: The sequel ⋮ Viscosity solutions of monotonic functional parabolic PDE ⋮ Existence and nonexistence of Fujita-type critical exponents for isotropic and anisotropic semi-linear parabolic systems ⋮ Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations ⋮ Local existence and nonexistence for reaction-diffusion systems with coupled exponential nonlinearities ⋮ Global nonexistence for the Cauchy problem of some nonlinear reaction-diffusion systems

Cites Work

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• A Cauchy problem for $u_t - \Delta u = u^p \ \hbox{with}\ 0 < p < 1$. Asymptotic behaviour of solutions
• Maximum principles and comparison theorems for semilinear parabolic systems and their applications

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