Parabolic equations with coefficients depending on t and parameters
T. Winiarska (1990)
Annales Polonici Mathematici
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T. Winiarska (1990)
Annales Polonici Mathematici
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Frank Neubrander (1989)
Semigroup forum
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R. de Laubenfels, F. Yao (1996)
Semigroup forum
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Tomasz Dlotko (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.
F. Neubrander (1984)
Semigroup forum
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Y.S. Eidelman, I.V. Tikhonov (1997)
Semigroup forum
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R. de Laubenfels, F. Yao (1997)
Semigroup forum
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R. de Laubenfels (1989)
Semigroup forum
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El-Fiky, Ahmed (1998)
International Journal of Mathematics and Mathematical Sciences
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J.R. Dorroh (1985)
Semigroup forum
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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. ...
Piotr Biler (1995)
Studia Mathematica
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The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
Yehuda Pinchover (1996)
Mathematische Zeitschrift
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