Transmission problems with nonlocal boundary conditions and rough dynamic interfaces

Gal, Ciprian G.; Warma, Mahamadi

doi:10.1088/0951-7715/29/1/161

Cited by 8 publications

(1 citation statement)

References 39 publications

(80 reference statements)

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“…In this case, it is standard to show by semigroup methods that the latter problem is also globally well-posed for each h > 0 (see, e.g., [24,25]). Our point is to observe that g h satisfies the same condition (4.3) and that the various constants involved in the estimates performed [18, Theorem 3.2 and Remark 3.3] are actually independent of t, T, and h. This procedure allows us to obtain an estimate like (4.5) uniformly in h > 0.…”

Section: Solvability In the Class Of Weak And Strong Solutionsmentioning

confidence: 99%

The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?

Gal

2015

Milan J. Math.

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In this study, we investigate reaction-diffusion and elliptic-like equations with two classes of dynamic boundary conditions, of reactive and reactivediffusive type. We provide sharp upper and lower bounds on the dimension of the global attractor in all these cases. In particular, we emphasize how surface diffusion can act as a damping force in reducing the degree of complexity in these systems. We obtain a new Weyl asymptotic law for eigenvalue sequences associated with a family of perturbed Wentzell operators which is of independent interest.Mathematics Subject Classification. Primary 35J66, 35K55; Secondary 35J15, 35K10.

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Section: Solvability In the Class Of Weak And Strong Solutionsmentioning

confidence: 99%

The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?

Gal

2015

Milan J. Math.

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Fractional-in-Time Semilinear Parabolic Equations and Applications

Gal¹,

Warma²

2020

Mathématiques Et Applications

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The Semilinear Parabolic Problem

Gal

Warma

2020

Mathématiques Et Applications

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Transmission problems with nonlocal boundary conditions and rough dynamic interfaces

Cited by 8 publications

References 39 publications

The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?

The Role of Surface Diffusion in Dynamic Boundary Conditions: Where Do We Stand?

Fractional-in-Time Semilinear Parabolic Equations and Applications

The Semilinear Parabolic Problem

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