Akkoyunlu, Ebubekir

This paper deals with the following Neumann initial-boundary value problem (Formula presented.) where (Formula presented.) (Formula presented.) is a bounded domain with smooth boundary, (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.), and (Formula presented.). The initial data satisfy (Formula presented.) where (Formula presented.), (Formula presented.), and (Formula presented.)  on (Formula presented.). We rigorously prove that the problem admits a unique global classical solution which is uniformly bounded in time if one of the following conditions holds: (Formula presented.) or (Formula presented.).

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Ayazoglu, Rabil; Simsek, Ramazan

This paper considers the global boundedness of solutions to the parabolic-elliptic chemotaxis system with a logistic source involving exponents that depend on spatial variables and nonlinear signal production: (Formula presented.) where (Formula presented.), μ, (Formula presented.), and (Formula presented.) is a measurable function, subject to the homogeneous Neumann boundary conditions in a bounded domain (Formula presented.) with smooth boundary. We prove that if either (Formula presented.), (Formula presented.) or (Formula presented.) with (Formula presented.) or (Formula presented.) with (Formula presented.), (Formula presented.) or (Formula presented.), then the above system possesses a unique global bounded classical solution.

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