Boundary characteristic point regularity for semilinear reaction-diffusion equations: towards an ODE criterion

DOI10.1007/s10958-011-0347-1zbMath1286.35123arXiv1106.4696OpenAlexW2002792613MaRDI QIDQ393303

Victor A. Galaktionov, Vladimir Gilelevich Maz'ya

Publication date: 17 January 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4696

zbMATH Keywords

homogeneous Dirichlet conditionsPetrovskii regularity criterion

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial-boundary value problems for second-order parabolic equations (35K20) Semilinear parabolic equations (35K58)

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Cites Work

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• An asymptotic theory of higher-order operator differential equations with nonsmooth nonlinearities
• On \(\sqrt{\log\log}\) blow-up in higher-order reaction-diffusion and wave equations: A formal ``geometric approach
• Regularity of solutions for the Navier-Stokes system of incompressible flows on a polygon
• Coefficients in the asymptotic solutions of the Cauchy boundary-value parabolic problems in domains with a conical point
• Wiener's criterion at \(\infty\) for the heat equation
• Boundedness of the gradient of a solution and Wiener test of order one for the biharmonic equation
• On regularity of a boundary point for higher-order parabolic equations: towards Petrovskii-type criterion by blow-up approach
• The initial-boundary value problems for the heat operator in non-cylindrical domains
• Sulproblema di Dirichlet per l'equazione del calore
• A stability technique for evolution partial differential equations. A dynamical systems approach
• Boundary properties of solutions of second-order parabolic equations in domains with special symmetry
• Wiener's criterion for the heat equation
• The Wiener test for higher order elliptic equations.
• Approaching a vertex in a shrinking domain under a nonlinear flow
• Blow-up in quasilinear parabolic equations. Transl. from the Russian by Michael Grinfeld
• On the regularity at shrinking points for the porous media equation
• Global solutions of higher-order semilinear parabolic equations in the supercritical range
• Asymptotic formula for solutions to elliptic equations near the Lipschitz boundary
• The zero set of a solution of a parabolic equation.
• The Green function and Poisson kernels of a parabolic problem in a domain with a conical point
• On the wiener type regularity of a boundary point for the polyharmonic operator
• SHARP HEAT-KERNEL ESTIMATES FOR HIGHER-ORDER OPERATORS WITH SINGULAR COEFFICIENTS
• Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients