On pseudo almost periodic solutions of the parabolic-elliptic Keller-Segel systems
-
Nguyen Thi Van
,
Tran Minh Nguyet
Abstract
In this paper, we investigate the existence, uniqueness and exponential stability of pseudo almost periodic (PAP-) mild solutions of the parabolic-elliptic (P-E) Keller-Segel system on a bounded domain Ω ∈ Rn with smooth boundary. First, the well-posedness of the corresponding linear system is established by using the smoothing estimates of the Neumann heat semigroup on Ω. Then, the existence of PAP-mild solution of linear system is done by proving a Massera-type principle. Next, we obtain the well-posedness of such solutions for semilinear system by using the results of linear system and fixed point arguments. The exponential stability is proven by using again the estimates of the Neumann heat semigroup. Finally, we also consider the Keller-Segel system on the real hyperbolic manifolds.
(Communicated by Giuseppe Di Fazio)
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Articles in the same Issue
- Joins of normal matrices, their spectrum, and applications
- On isbell’s density theorem for bitopological pointfree spaces II
- Every positive integer is a sum of at most n + 2 centered n-gonal numbers
- A generalisation of q-additive functions
- Generalised class groups in dihedral and fake ℤp-extensions
- Singular value bounds with applications to norm and numerical radius inequalities
- Coefficient bounds for convex functions associated with cosine function
- On solutions to q-difference equations for q-appell functions in the spirit of Olsson and Exton
- Numerical implementation of solving a boundary value problem including both delay and parameter
- Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions
- Global attractivity of nonlinear delay dynamic equations on time scales via Lyapunov functional method
- On pseudo almost periodic solutions of the parabolic-elliptic Keller-Segel systems
- A note on derivations into annihilators of the ideals of banach algebras
- Characterization of nonlinear mixed skew lie and jordan n-Type derivation on ∗-Algebras
- Linear and uniformly continuous surjections between Cp-spaces over metrizable spaces
- A goodness-of-fit test for testing exponentiality based on normalized dynamic survival extropy
- Monotonicity results of ratio between two normalized remainders of Maclaurin series expansion for square of tangent function
