Tikhonov-Petrovskii problem for second-order parabolic equations

DOI10.1007/BF00968068zbMath0501.35040MaRDI QIDQ1172206

B. N. Khimchenko, L. I. Kamynin

Publication date: 1981

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

uniquenessmethod of barrier functionsCauchy's problemnonnegative characteristic formTikhonov-Petrovskii problemTikhonov-Taecklind class

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for second-order parabolic equations (35K15)

Related Items (10)

On a nonlinear nonlocal parabolic problem ⋮ Unilateral estimates for solutions to the second and third boundary value problems (with oblique derivative) for a strongly dissipative second-order parabolic equation ⋮ Supremum principles for the higher-order derivatives of solutions to the Dirichlet problem for parabolic equations without compatibility conditions between the data ⋮ Dissipative effect for second-order parabolic operators ⋮ Solvability of the Cauchy problem for a parabolic equation with unbounded coefficients ⋮ Uniqueness classes of solutions of boundary value problems for nondivergent second order parabolic equations in noncylindrical domains ⋮ An approach to the uniqueness problem for second-order parabolic equations ⋮ Uniqueness of the solution of the Cauchy problem for parabolic systems ⋮ Pseudo-differential operators with meromorphic symbols and systems of complex differential equations ⋮ On some isomorphism generated by a~linear parabolic equation

Cites Work

• r-inscribed curves
• A priori estimates for the solutions of second-order parabolic equations near the lower cap of the parabolic boundary
• Increasing solutions of linear second-order equations with nonnegative characteristic form
• Uniqueness in the Cauchy Problem for Parabolic Equations
• Sur les solutions des équations du type parabolique déterminées dans une région illimitée

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