In this paper, we study the Moore-Gibson-Thompson equation in R N , which is a third order in time equation that arises in viscous thermally relaxing fluids and also in viscoelastic materials (then under the name of standard linear viscoelastic model). First, we use some Lyapunov functionals in the Fourier space to show that, under certain assumptions on some parameters in the equation, an energy norm related with the solution decays with a rate (1 + t) −N/4 . But this does not give the decay rate of the solution itself. Hence, in the second part of the paper, we show an explicit representation of the solution in the frequency domain by analyzing the eigenvalues of the Fourier image of the solution and writing the solution accordingly. We use this eigenvalues expansion method to give the decay rate of the solution (and its derivatives), which (for the solution) results in (1 + t) 1−N/4 for N = 1, 2 and (1 + t) 1/2−N/4 when N ≥ 3.

We study the third order in time linear dissipative wave equation known as the Moore-Gibson-Thompson equation, that appears as the linearization of a the Jordan-Moore-Gibson-Thompson equation, an important model in nonlinear acoustics. The same equation also arises in viscoelasticity theory, as a model which is considered more realistic than the usual Kelvin-Voigt one for the linear deformations of a viscoelastic solid. In this context, it is known as the Standard Linear Viscoelastic model. We complete the description in [13] of the spectrum of the generator of the corresponding group of operators and show that, apart from some exceptional values of the parameters, this generator can be made to be a normal operator with a new scalar product, with a complete set of orthogonal eigenfunctions. Using this property we also obtain optimal exponential decay estimates for the solutions as t → ∞, whether the operator is normal or not.

Adverse reactions to capecitabine-based chemotherapy limit full administration of cytotoxic agents. Likewise, genetic variations associated with capecitabine-related adverse reactions are associated with controversial results and a low predictive value. Thus, more evidence on the role of these variations is needed. We evaluated the association between nine polymorphisms in MTHFR, CDA, TYMS, ABCB1, and ENOSF1 and adverse reactions, dose reductions, treatment delays, and overall toxicity in 239 colorectal cancer patients treated with capecitabine-based regimens. The ABCB1*1 haplotype was associated with a high risk of delay in administration or reduction in the dose of capecitabine, diarrhea, and overall toxicity. CDA rs2072671 A was associated with a high risk of overall toxicity. TYMS rs45445694 was associated with a high risk of delay in administration or reduction in the dose of capecitabine, HFS >1 and HFS >2. Finally, ENOSF1 rs2612091 was associated with HFS >1, but was a poorer predictor than TYMS rs45445694. A score based on ABCB1-CDA polymorphisms efficiently predicts patients at high risk of severe overall toxicity (PPV, 54%; sensitivity, 43%) in colorectal cancer patients treated with regimens containing capecitabine. Polymorphisms in ABCB1, CDA, ENOSF1,and TYMS could help to predict specific and overall severe adverse reactions to capecitabine.

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In this paper we consider a linear wave equation with strong damping and dynamical boundary conditions as an alternative model for the classical spring-mass-damper ODE. Our purpose is to compare analytically these two approaches to the same physical system. We take a functional analysis point of view based on semigroup theory, spectral perturbation analysis and dominant eigenvalues.  2004 Elsevier Inc. All rights reserved.