𝐿^{𝑝}-𝐿^{𝑞} decay estimates for the Cauchy problem of linear thermoelastic systems with second sound in one space variable

Lin, Yong; Wang, Yaguang

doi:10.1090/s0033-569x-06-00989-6

Cited by 17 publications

(12 citation statements)

References 21 publications

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“…This lemma follows from the results of Yang & Wang [24], in particular from the expansions of the characteristic values; cp. similar results for classical thermoelasticity in [8,Thm.3.6], going back to Kawashima [11].…”

Section: Decay Rates Of Global Solutionsmentioning

confidence: 76%

“…Having given the global solution for small data (u x , u t , θ, q)(t = 0) in H 2 from Tarabek [19], we shall describe in Section 4 the asymptotic behavior of V (t) ≡ (u x , u t , θ, q)(t) as time t → ∞. For the corresponding linearized system Yang and Wang [24], also W. Wang and Z. Wang [21], gave decay rates for L q -norms of V (t) (cp. also Wang and Yang [23] in three space dimensions).…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Well-Posedness and Rates of Decay in Thermoelasticity With Second Sound

Racke

Wang

2008

J. Hyper. Differential Equations

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We consider the Cauchy problem in nonlinear thermoelasticity with second sound in one space dimension. Due to Cattaneo's law, replacing Fourier's law for heat conduction, the system is hyperbolic. We first investigate the local well-posedness as a strictly hyperbolic system, and then discuss the relation between energy estimates for non-symmetric hyperbolic systems and well-posedness. For the global small solution we describe the long time behavior and obtain decay rates of the L 2 -norm.

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Section: Decay Rates Of Global Solutionsmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Nonlinear Well-Posedness and Rates of Decay in Thermoelasticity With Second Sound

Racke

Wang

2008

J. Hyper. Differential Equations

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“…The model based on Cattaneo's law is called thermoelastic system with second sound which is very important in some applications. (1.1) has been studied widely by many authors (see [4,[7][8][9]11]). For example, in [9], by energy method, the existence of smooth solution to linear thermoelastic system with second sound in two cases is proved in one space variable.…”

Section: Mathematical Model and Main Resultsmentioning

confidence: 99%

The pointwise estimates to solutions for 1-dimensional linear thermoelastic system with second sound

Wang

2007

Journal of Mathematical Analysis and Applications

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In this paper, we study the thermoelastic system with second sound in one space variable. The mathematical model is a hyperbolic partial differential system with damping term which brings about some parabolic properties. The pointwise estimates of the solution are obtained and from which the generalized Huygens' principle is shown. Our approach is based on detailed analysis on the Green function of the system. Mathematical model and main resultIn this paper, we study the following 1-dimensional thermoelastic system with second sound:where u and θ are the displacement and temperature difference of the elastic media, respectively, q denotes the heat flux, κ, τ, α, β, γ are positive constants.

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“…with k 12 , k 21 and k 22 being 4 × 2, 2 × 4 and 2 × 2 matrices respectively, which will be determined later, we have that…”

Section: Decoupling the Principal Terms In System (11)mentioning

confidence: 99%

Propagation of singularities for Cauchy problems of semilinear thermoelastic systems with microtemperatures

Lin¹,

Huang

2010

Mathematische Nachrichten

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The propagation of singularities of solutions to the Cauchy problem of a semilinear thermoelastic system with microtemperatures in one space variable is studied. First, by using a diagonalization argument of phase space analysis, the coupled thermoelastic system with microtemperatures will be decoupled microlocally. Second, using a classical bootstrap argument, the property of finite propagation speed of singularities for the semilinear thermoelastic system is obtained. Finally, it is also shown that the microlocal weak singularities propagate along the null bicharacteristics of the hyperbolic operators of the coupled semilinear system.

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𝐿^{𝑝}-𝐿^{𝑞} decay estimates for the Cauchy problem of linear thermoelastic systems with second sound in one space variable

Cited by 17 publications

References 21 publications

Nonlinear Well-Posedness and Rates of Decay in Thermoelasticity With Second Sound

Nonlinear Well-Posedness and Rates of Decay in Thermoelasticity With Second Sound

The pointwise estimates to solutions for 1-dimensional linear thermoelastic system with second sound

Propagation of singularities for Cauchy problems of semilinear thermoelastic systems with microtemperatures

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