Displaying similar documents to “Smooth Dependence on Initial Data of Mild Solutions to Evolution Equations”

Semilinear Cauchy Problems with Almost Sectorial Operators

Tomasz Dlotko (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

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.

The Kneser property for the abstract Cauchy problem

Hernán R. Henríquez, Genaro Castillo G. (2003)

Annales Polonici Mathematici

Similarity:

We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.

Cauchy problem for semilinear parabolic equations with initial data in H (R) spaces.

Francis Ribaud (1998)

Revista Matemática Iberoamericana

Similarity:

We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂U - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces H (R). In most of the studies on this subject, the initial data U(x) belongs to Lebesgue spaces L(R) or to supercritical fractional Sobolev spaces H (R) (s > n/p). Our purpose is to study the intermediate cases (namely for 0 < s < n/p). We give some mapping properties for functions with polynomial...

On the Cauchy problem for linear PDEs with retarded arguments at derivatives

Krzysztof A. Topolski (2015)

Annales Polonici Mathematici

Similarity:

We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.