Egberts, Ginger Vermolen, Fred van Zuijlen, Paul
Published in
Journal of Mathematical Biology

To deal with permanent deformations and residual stresses, we consider a morphoelastic model for the scar formation as the result of wound healing after a skin trauma. Next to the mechanical components such as strain and displacements, the model accounts for biological constituents such as the concentration of signaling molecules, the cellular dens...

Wang, Qin Song, Kyungwoo
Published in
Acta Mathematica Scientia

We are concerned with the shock diffraction configuration for isothermal gas modeled by the conservation laws of nonlinear wave system. We reformulate the shock diffraction problem into a linear degenerate elliptic equation in a fixed bounded domain. The degeneracy is of Keldysh type—the derivative of a solution blows up at the boundary. We establi...

Fernández-Romero, A. Guillén-González, F. Suárez, A.
Published in
Zeitschrift für angewandte Mathematik und Physik

In this paper, we study a PDE–ODE system as a simplification of a glioblastoma model. Mainly, we prove the existence and uniqueness of global in time classical solution using a fixed point argument. Moreover, we show some stability results of the solution depending on some conditions on the parameters.

Paronetto, Fabio
Published in
Calculus of Variations and Partial Differential Equations

In this note we give existence results for the generalized Tricomi equations Ru′′+Bu=f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {R}}u'' + {\mathcal {B}}...

Hu, Rentian Edwards, Thomas K. Smith, Leslie M. Stechmann, Samuel N.
Published in
Research in the Mathematical Sciences

Asymptotic models have provided valuable insight into the atmosphere and its dynamics. Nevertheless, one shortcoming of the classic asymptotic models, such as the quasi-geostrophic (QG) equations, is that they describe a “dry” atmosphere and do not account for water vapor, clouds, and rainfall. Recently, precipitating QG (PQG) equations were derive...

Paronetto, Fabio
Published in
Calculus of Variations and Partial Differential Equations

We give an existence result for first order evolution equation of the type Ru′+Au=f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {R}u' + \mathcal {A}u = f$$\...

Tong, Lining Sun, Yanyan
Published in
Chinese Annals of Mathematics, Series B

The one-dimensional compressible non-Newtonian models are considered in this paper. The extra-stress tensor in our models satisfies a kind of power law structure which was proposed by O. A. Ladyzhenskaya in 1970s. In particular, the viscosity coefficient in our models depends on the density. By using energy-estimate, the authors obtain the existenc...

Bae, Myoungjean Xiang, Wei

In this paper, we review a result from [1] on the existence of detached shock solutions of steady potential flow past a convex blunt body inR2, and summarize its proof. Furthermore, we discuss an open problem about detached shock solutions of full Euler system, and explain its difficulties.

Fan, Jishan Ozawa, Tohru
Published in
Journal of Mathematical Fluid Mechanics

We study the initial boundary value problem for the three-dimensional modified compressible Navier–Stokes–Fourier equations proposed by Brenner. We establish a blow-up criterion for local strong solutions in terms of the density ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usep...

Cirilo, Eliandro Petrovskii, Sergei Romeiro, Neyva Natti, Paulo
Published in
International Journal of Applied and Computational Mathematics

Reaction-telegraph equation (RTE)—a nonlinear partial differential equation of mixed parabolic-hyperbolic type—is believed to be a better mathematical framework to describe population dynamics than the more traditional reaction–diffusion equations. Being motivated by ecological problems such as habitat fragmentation and alien species introduction (...