## Computational and Applied Mathematics Seminar

**Spring 2018**

**Mondays at 4:10 p.m. in 401 Carver
**

The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.

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03/19

**LOCAL HOLDER REGULARITY FOR QUASILINEAR
PARABOLIC EQUATISON**

**Sukung Huang **

Department of Mathematics

Yonsei University, South Korea

**Abstract: ** For parabolic p-Laplacian type of equations, where the structure is generalized in Orlicz space, we deliver H\"{o}lder regularity for degenerate and singular type of equations using a unified method of proof relying on geometric characters. Also I will explain recent results of H\"{o}lder regularity for porous medium type of equations. This result also explains local regularity of a

coupled system consisting of a degenerate porous medium type of Keller-Segel system and Stokes system modeling the motion of swimming bacteria living in a fluid and consuming oxygen.

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02/26

**Inverse resonance problems for the SchrÃ¶dinger operator on the real line with mixed given data**

**Xiao-Chuan Xu**

Nanjing University of Science and Technology

**Abstract:** In this work, we study inverse resonance problems for the SchrÃ¶dinger

operator on the real line with the potential supported in [0, 1]. In general, all eigenvalues

and resonances cannot uniquely determine the potential. (i) It is shown that if the

potential is known a priori on [0, 1/2], then the unique recovery of the potential on

the whole interval from all eigenvalues and resonances is valid. (ii) If the potential

is known a priori on [0, a], then for the case a > 1/2, infinitely many eigenvalues

and resonances can be missing for the unique determination of the potential, and for

the case a < 1/2, all eigenvalues and resonances plus a part of so-called sign-set

can uniquely determine the potential. (iii) It is also shown that all eigenvalues and

resonances, together with a set of logarithmic derivative values of eigenfunctions and

wave-functions at 1/2, can uniquely determine the potential.

03/05

**Positive and free energy satisfying schemes for diffusion with interaction potentials**

**Wumaier Maimaitiyiming**

Department of Mathematics, ISU

**Abstract: ** Aggregation and chemotaxis are important phenomena in biology, and they can be modeled by a class of diffusion equations with interaction potentials. In this work, we design and analyze a second order accurate free energy satisfying finite volume method for solving such equations. The schemes (both semi-discrete and fully discrete) are shown to satisfy free energy dissipation law, preserve non-negativity for the solution and conserve total mass at discrete level. These properties guarantee that computed numerical solutions are probability density, and schemes are energy stable. One and two-dimensional numerical examples are given to demonstrate the effectiveness of the scheme.

03/19

**LOCAL HOLDER REGULARITY FOR QUASILINEAR
PARABOLIC EQUATISON**

**Sukung Huang **

Department of Mathematics

Yonsei University, South Korea

E-mail address: sukjung hwang@yonsei.ac.kr

**Abstract: ** For parabolic p-Laplacian type of equations, where the structure is generalized in Orlicz space, we deliver H\"{o}lder regularity for degenerate and singular type of equations using a unified method of proof relying on geometric characters. Also I will explain recent results of H\"{o}lder regularity for porous medium type of equations. This result also explains local regularity of a

coupled system consisting of a degenerate porous medium type of Keller-Segel system and Stokes system modeling the motion of swimming bacteria living in a fluid and consuming oxygen.

3/26

**Hongxin Chen**

Department of ECE, Iowa State Univ.

04/02

**Russell Schwabb **

Michigan State University

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