Improving the parabolic equation solution for problems involving poro‐elastic media.

2010 ◽  
Vol 127 (3) ◽  
pp. 1962-1962
Author(s):  
Adam M. Metzler ◽  
William L. Siegmann ◽  
Michael D. Collins ◽  
Ralph N. Baer ◽  
Jon M. Collis
Keyword(s):  
Parabolic Equation ◽  
Elastic Media ◽  
Equation Solution

scholarly journals Global in Time Results for a Parabolic Equation Solution in Non-rectangular Domains

2020 ◽  
pp. 257-274 ◽  
Author(s):  
Louanas Bouzidi ◽  
Arezki Kheloufi
Keyword(s):  
Parabolic Equation ◽  
Sobolev Space ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Dirichlet Boundary ◽  
Global Regularity ◽  
Interpolation Inequality ◽  
Dirichlet Boundary Conditions ◽  
Energy Estimates ◽  
Equation Solution

This article deals with the parabolic equation ∂tw − c(t)∂2x w = f in D, D = { (t, x) ∈ R2 : t > 0, φ1 (t) < x < φ2(t) } with φi : [0,+∞[→ R, i = 1, 2 and c : [0,+∞[→ R satisfying some conditions and the problem is supplemented with boundary conditions of Dirichlet-Robin type. We study the global regularity problem in a suitable parabolic Sobolev space. We prove in particular that for f ∈ L2(D) there exists a unique solution w such that w, ∂tw, ∂jw ∈ L2(D), j = 1, 2. Notice that the case of bounded non-rectangular domains is studied in [9]. The proof is based on energy estimates after transforming the problem in a strip region combined with some interpolation inequality. This work complements the results obtained in [19] in the case of Cauchy-Dirichlet boundary conditions

A variable rotated parabolic equation for elastic media

2004 ◽  
Vol 115 (5) ◽  
pp. 2579-2579
Author(s):  
Donald A. Outing ◽  
William L. Siegmann ◽  
Michael D. Collins
Keyword(s):  
Parabolic Equation ◽  
Elastic Media

Wide-Angle Parabolic Equation Solution of Ocean Acoustic Propagation with Lossy Penetrable Bottom

1999 ◽  
Vol 38 (Part 1, No. 5B) ◽  
pp. 3361-3365 ◽  
Author(s):  
Masuya Hada ◽  
Taro Fujii ◽  
Takenobu Tsuchiya ◽  
Tetsuo Anada ◽  
Nobuyuki Endoh
Keyword(s):  
Parabolic Equation ◽  
Acoustic Propagation ◽  
Wide Angle ◽  
Equation Solution

Energy‐conserving and single‐scattering parabolic equation solutions for elastic media

2003 ◽  
Vol 114 (4) ◽  
pp. 2428-2428
Author(s):  
Elizabeth T. Kusel ◽  
William L. Siegmann ◽  
Michael D. Collins ◽  
Joseph F. Lingevitch
Keyword(s):  
Parabolic Equation ◽  
Single Scattering ◽  
Elastic Media ◽  
Energy Conserving
Sign in / Sign up

Export Citation Format

Share Document