Funkcialaj Ekvacioj

Global Existence and Decay Estimates for Quasilinear Wave Equations with Nonuniform Dissipative Term

Tomonari Watanabe

2015 Volume 58 Issue 1 Pages 1-42
Published: 2015
Released on J-STAGE: April 09, 2015

DOIhttps://doi.org/10.1619/fesi.58.1

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In this paper, we study a Cauchy problem for quasilinear wave equations with dissipative term in Sobolev space H^L × H^L-1 (L ≥ [d/2] + 3). The coefficients of the dissipative term depends on space variables and may vanish in some compact region. In order to control the derivatives of the dissipative coefficients, we introduce a rescaling argument. Using the argument, we obtain a global existence theorem and decay estimates with additional assumptions for the initial data.

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On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations

Tetu Makino

2015 Volume 58 Issue 1 Pages 43-85
Published: 2015
Released on J-STAGE: April 09, 2015

DOIhttps://doi.org/10.1619/fesi.58.43

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We consider spherically symmetric motions of inviscid compressible gas surrounding a solid ball under the gravity of the core. Equilibria touch the vacuum with finite radii, and the linearized equation around one of the equilibria has time-periodic solutions. To justify the linearization, we should construct true solutions for which this time-periodic solution plus the equilibrium is the first approximation. But this leads us to difficulty caused by singularities at the free boundary touching the vacuum. We solve this problem by the Nash-Moser theorem.

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Center Manifold Theorem and Stability for Integral Equations with Infinite Delay

Hideaki Matsunaga, Satoru Murakami, Yutaka Nagabuchi, Nguyen Van Minh

2015 Volume 58 Issue 1 Pages 87-134
Published: 2015
Released on J-STAGE: April 09, 2015

DOIhttps://doi.org/10.1619/fesi.58.87

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The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the variation-of-constants formula in the phase space that is obtained in our previous paper [22] (Funkcial. Ekvac. 55 (2012), 479-520). Furthermore, we prove a stability reduction principle by which the stability of an autonomous integral equation is implied by that of an ordinary differential equation which we call the "central equation".

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Viscosity Solutions of Systems of Variational Inequalities with Interconnected Bilateral Obstacles

Boualem Djehiche, Said Hamadène, Marie-Amelie Morlais

2015 Volume 58 Issue 1 Pages 135-175
Published: 2015
Released on J-STAGE: April 09, 2015

DOIhttps://doi.org/10.1619/fesi.58.135

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We study a general class of nonlinear second-order variational inequalities with interconnected bilateral obstacles, related to a multiple modes switching game. Under rather weak assumptions, using systems of penalized unilateral backward SDEs, we construct a continuous viscosity solution of polynomial growth. Moreover, we establish a comparison result which in turn yields uniqueness of the solution.

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