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Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2009, Volume 32, Issue 5, pp. 505 - 534
In this paper, we consider nonlinear thermoelastic systems of Timoshenko type in a one‐dimensional bounded domain. The system has two dissipative mechanisms... 
Timoshenko systems | global existence | exponential decay | thermoelasticity | second sound | nonlinearity | Global existence | Nonlinearity | Second sound | Thermoelasticity | Exponential decay | SMOOTH SOLUTIONS | MATHEMATICS, APPLIED | ENERGY | DECAY | STABILIZATION | BEAM | FEEDBACK | Mathematics - Analysis of PDEs
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2015, Volume 259, Issue 12, pp. 7578 - 7609
This paper deals with a boundary-value problem in two-dimensional smoothly bounded domains for the coupled Keller–Segel–Stokes system Here, one of the... 
Keller–Segel–Stokes system | Global existence | Tensor-valued sensitivity | Boundedness | Keller-Segel-Stokes system | MATHEMATICS | CHEMOTAXIS-FLUID MODEL | STABILIZATION | EQUATIONS | NONLINEAR DIFFUSION | BLOW-UP | WEAK SOLUTIONS | DOMAINS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2016, Volume 261, Issue 9, pp. 4944 - 4973
In this paper we continue to deal with the initial–boundary value problem for the coupled Keller–Segel–Stokes system where is a bounded domain with smooth... 
Keller–Segel–Stokes system | Global existence | Tensor-valued sensitivity | Boundedness | MATHEMATICS | CHEMOTAXIS-FLUID MODEL | Keller-Segel-Stokes system | DECAY | BEHAVIOR | FINITE-TIME BLOWUP | EQUATIONS | NONLINEAR DIFFUSION | DOMAINS | Differential equations
Journal Article
Ecological Complexity, ISSN 1476-945X, 03/2015, Volume 21, pp. 199 - 214
In this paper, first we consider the global dynamics of a ratio-dependent predator–prey model with density dependent death rate for the predator species.... 
Chaos | Predator–prey | Spatial pattern | Global bifurcation | Globally stable homogeneous steady-state | Predator-prey | SYSTEM | PLANKTON | SPATIOTEMPORAL CHAOS | MUTUAL INTERFERENCE | COEXISTENCE | STABILITY ANALYSIS | HYPOTHESIS | DYNAMICS | TURING INSTABILITIES | ECOLOGY | BIFURCATION-ANALYSIS
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 04/2017, Volume 19, Issue 2, p. 1650038
In this paper, we construct for every α > 0 and λ ∈ ℂ a class of initial values u 0 for which there exists a local solution of the nonlinear Schrödinger... 
Local existence | Global existence | Nonlinear Schrödinger equation | Scattering | MATHEMATICS | MATHEMATICS, APPLIED | global existence | scattering | Nonlinear Schrodinger equation | local existence | CAUCHY-PROBLEM | Analysis of PDEs | Mathematics
Journal Article
1994, Lecture notes in mathematics, ISBN 0387577033, Volume 1570, xv, 234
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of... 
Functional analysis | Linear operators | Evolution equations | Global analysis (Mathematics) | Analysis
Book
Journal of Functional Analysis, ISSN 0022-1236, 03/2016, Volume 270, Issue 5, pp. 1663 - 1683
We consider the Keller–Segel system coupled with the Navier–Stokes fluid in the whole space, and prove the existence of global mild solutions with the small... 
Navier–Stokes equations | Asymptotic stability | Keller–Segel system | Self-similar solutions | Existence of global mild solutions | Continuous dependence for the initial data | Keller-Segel system | Navier-Stokes equations | MODEL | PARABOLIC-PARABOLIC TYPE | MATHEMATICS | R-N | WEAK SOLUTIONS | INITIAL DATA | DOMAINS | Fluid dynamics
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 4/2019, Volume 70, Issue 2, pp. 1 - 27
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 951 - 958
This paper is concerned with the existence of global in time solutions of a time fractional reaction–diffusion system with time fractional derivatives.... 
Balance law | Global existence | Reaction–diffusion equations | Fractional calculus | Asymptotic behavior | MATHEMATICS, APPLIED | EQUATIONS | Reaction-diffusion equations
Journal Article
Neurocomputing, ISSN 0925-2312, 03/2019, Volume 332, pp. 259 - 269
In this paper, we are concerned with a class of Clifford-valued inertial Cohen-Grossberg neural networks with time-varying delays. Based on the coincidence... 
Global exponential stability | Inertial Cohen–Grossberg neural networks | Clifford algebra | Anti-periodic solutions | SYNCHRONIZATION | MODELS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Inertial Cohen-Grossberg neural networks | Neural networks | Algebra
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 12/2017, Volume 74, Issue 12, pp. 3024 - 3041
In this paper, we consider the following nonlinear wave equation with variable exponents: where are positive constants. By using the Faedo–Galerkin method, the... 
Blow up | Variable nonlinearity | Existence | Nonlinear damping | MATHEMATICS, APPLIED | SOBOLEV EMBEDDINGS | VARIABLE EXPONENT | PARABOLIC EQUATIONS | SPACES | EVOLUTION-EQUATIONS | GLOBAL NONEXISTENCE THEOREMS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 01/2019, Volume 341, pp. 80 - 92
In the previous article (Yoshikawa, 2017), the author proposes the energy method for structure-preserving finite difference schemes, which enable us to show... 
Small data global existence | Unconditional error estimate |