Displaying similar documents to “On the Cauchy problem for a second order semilinear parabolic equation with factored linear part.”

Semilinear Cauchy Problems with Almost Sectorial Operators

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.

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. ...

The Cauchy problem and self-similar solutions for a nonlinear parabolic equation

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.