Viscosity solutions of fully nonlinear functional parabolic PDE.

Liu, Wei-An; Lu, Gang

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Displaying similar documents to “Viscosity solutions of fully nonlinear functional parabolic PDE.”

Parabolic differential-functional inequalities in viscosity sense

Krzysztof Topolski (1998)

Annales Polonici Mathematici

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We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.

On the vanishing viscosity method for first order differential-functional IBVP

Krzysztof A. Topolski (2008)

Czechoslovak Mathematical Journal

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We consider the initial-boundary value problem for first order differential-functional equations. We present the `vanishing viscosity' method in order to obtain viscosity solutions. Our formulation includes problems with a retarded and deviated argument and differential-integral equations.

Parabolic equations relative to vector fields.

Bieske, Thomas (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Boundary behaviour in strongly degenerate parabolic equations.

Winkler, M. (2003)

Acta Mathematica Universitatis Comenianae. New Series

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Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations.

Crandall, M.G., Kocan, M., Lions, P.L., Świȩch, A. (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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A generalization of the maximum principle to nonlinear parabolic systems

Dmitry Portnyagin (2003)

Annales Polonici Mathematici

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A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.

Uniqueness of positive solutions of parabolic equations with unbounded coefficients

D. G. Aronson, P. Besala (1967)

Colloquium Mathematicae

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Comparison theorems for purely non-linear parabolic differential operators

P. Besala (1983)

Annales Polonici Mathematici

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The vanishing viscosity method in infinite dimensions

Piermarco Cannarsa, Giuseppe Da Prato (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.

Hamilton-Jacobi equations for control problems of parabolic equations

Sophie Gombao, Jean-Pierre Raymond (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power ${(- A)}^{β}$ – where is an unbounded operator in a Hilbert space – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already...