Uniqueness of solutions of a mixed problem for parabolic differential-functional equations
J. Szarski (1973)
Annales Polonici Mathematici
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J. Szarski (1973)
Annales Polonici Mathematici
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P. Besala, G. Paszek (1980)
Annales Polonici Mathematici
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Jacek Szarski (1974)
Annales Polonici Mathematici
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Liu, Wei-An, Lu, Gang (2005)
International Journal of Mathematics and Mathematical Sciences
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A. Fitzke (1975)
Annales Polonici Mathematici
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J. Szarski (1975)
Annales Polonici Mathematici
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Milena Matusik (2012)
Annales Polonici Mathematici
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The paper deals with the initial boundary value problem of Robin type for parabolic functional differential equations. The unknown function is the functional variable in the equation and the partial derivatives appear in the classical sense. A theorem on the existence of a classical solution is proved. Our formulation and results cover differential equations with deviated variables and differential integral problems.
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. ...
Agnieszka Bartłomiejczyk, Henryk Leszczyński (2014)
Annales Polonici Mathematici
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We consider the Cauchy problem for nonlinear parabolic equations with functional dependence. We prove Schauder-type existence results for unbounded solutions. We also prove existence of maximal solutions for a wide class of differential functional equations.
A. Voigt (1979)
Numerische Mathematik
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Z. Kowalski (1968)
Annales Polonici Mathematici
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Vladimír Ďurikovič (1979)
Annales Polonici Mathematici
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Anna Pudełko (2007)
Annales Polonici Mathematici
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We consider the initial value problem for an infinite system of differential-functional equations of parabolic type. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. The solutions are obtained by the monotone iterative method. We prove theorems on weak partial differential-functional inequalities as well the existence and uniqueness theorems in the class of continuous bounded functions and in the class of...
Topoloski, Krzysztof A. (1998)
Abstract and Applied Analysis
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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.
Agnieszka Bartłomiejczyk (2007)
Annales Polonici Mathematici
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We consider the Cauchy problem for nonlinear parabolic equations with functional dependence represented by the Hale functional acting on the unknown function and its gradient. We prove convergence theorems for a general quasilinearization method in natural subclasses of unbounded solutions.
Piotr Biler (2006)
Banach Center Publications
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This note contains some remarks on the paper of Y. Naito concerning the parabolic system of chemotaxis and published in this volume.
Bouziani, Abdelfatah (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Bieske, Thomas (2008)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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H. Ugowski (1971)
Annales Polonici Mathematici
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