Existence and uniqueness to the Cauchy problem for linear and
          semilinear parabolic equations with local conditions⋆

Gerardo Rubio

Displaying similar documents to “Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆”

Global Carleman estimate for stochastic parabolic equations, and its application

Xu Liu (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls for backward...

Optimality conditions for semilinear parabolic equations with controls in leading term

Hongwei Lou (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.

On the Cauchy problem for a degenerate parabolic differential equation.

El-Fiky, Ahmed (1998)

International Journal of Mathematics and Mathematical Sciences

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Existence of solutions for infinite systems of parabolic equations with functional dependence

Anna Pudełko (2005)

Annales Polonici Mathematici

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The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method. ...

Da Prato-Zabczyk's maximal inequality revisited. I.

Jan Seidler (1993)

Mathematica Bohemica

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Existence, uniqueness and regularity of mild solutions to semilinear nonautonomous stochastic parabolic equations with locally lipschitzian nonlinear terms is investigated. The adopted approach is based on the factorization method due to Da Prato, Kwapień and Zabczyk.

Uniqueness of positive solutions of parabolic equations with unbounded coefficients

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

Colloquium Mathematicae

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Global existence and long-time behavior of solutions to a class of degenerate parabolic equations

Cung The Anh, Phan Quoc Hung (2008)

Annales Polonici Mathematici

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We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.

Abstract parabolic problems with non-Lipschitz critical nonlinearities

Konrad J. Wąs (2010)

Colloquium Mathematicae

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The Cauchy problem for a semilinear abstract parabolic equation is considered in a fractional power scale associated with a sectorial operator appearing in the linear main part of the equation. Existence of local solutions is proved for non-Lipschitz nonlinearities satisfying a certain critical growth condition.