Registered Data

[CT028]

[02575] Propagation of Nonlinear Waves in Non-genuinely Nonlinear Characteristic Field

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : We consider a quasilinear hyperbolic system of partial differential equations to discuss the evolution of weakly nonlinear waves, where the evolution equation includes quadratic, cubic, and quartic nonlinear terms and the flux function admits two inflection points. We present an example from gasdynamics with analytical and numerical results demonstrating a wide range of wave phenomena, and study the interaction of expansion and compression waves evolving from a rectangular pulse.
  • Classification : 35B40, 35B65, 35C20, 35L65, 35L67
  • Author(s) :
    • Triveni Prasad Shukla (National Institute of Technology Warangal)

[01797] Random dynamics of 2D stochastic Naiver-Stokes equations on the whole space

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : In this talk, we consider the 2D stochastic Navier-Stokes equations (SNSE) driven by a linear multiplicative white noise of It\^o type on the whole space. Firstly, we will discuss the existence of a unique bi-spatial $(\mathbb{L}^2(\mathbb{R}^2),\mathbb{H}^1(\mathbb{R}^2))$-pullback random attractor for non-autonomous SNSE with initial data in $\mathbb{L}^2(\mathbb{R}^2)$. Finally, we will discuss the existence of an invariant measure for 2D autonomous SNSE. Also, the uniqueness of invariant measures for $\boldsymbol{f}=\mathbf{0}$ will be addressed.
  • Classification : 35B41, 35Q35, 37L55, 37N10, 35R60
  • Author(s) :
    • Kush Kinra (Indian Institute of Technology Roorkee, Roorkee)
    • Manil T. Mohan (Indian Institute of Technology Roorkee, Roorkee)

[01348] Existence and nonexistence of solutions of thin-film equations with variable exponent spaces

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : This works aims at presenting a thin film problem involving variable exponent sources in a bounded domain. Which deals with the existence and nonexistence of solutions under subcritical initial energy. Also determine the global existence of solutions, exponential decay and finite time blow-up of solutions under specific conditions for the proposed model.
  • Classification : 35B44, 35D30, 35K70
  • Author(s) :
    • GNANAVEL Soundararajan (Central University of Kerala)
    • GNANAVEL SOUNDARARAJAN (Central University of Kerala)

[01831] A cancer invasion model involving chemotaxis and haptotaxis

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : We present a cancer invasion model involving chemotaxis and haptotaxis in two spatial dimensions. This model comprises two parabolic PDEs and an ODE, which describe the degradation of the extracellular matrix ECM by matrix degrading enzymes secreted by tumor cells, and incorporates self-remodeling of the ECM. We establish global existence and uniqueness of classical solutions in the high cell proliferation regime.
  • Classification : 35B45, 35K55, 35Q92, 92C17
  • Author(s) :
    • Peter Pang (National University of Singapore)

[00698] Rigidity for Sobolev inequalities and radial PDEs on Cartan-Hadamard manifolds

  • Session Date & Time : 4E (Aug.24, 17:40-19:20)
  • Type : Contributed Talk
  • Abstract : We aim at classifying all the Cartan-Hadamard manifolds supporting an optimal function for the $p$-Sobolev inequality. We prove that, under the validity of the Cartan-Hadamard conjecture, which is known to be true in dimension $n\le 4$, the only such manifold is $\mathbb{R}^n$, up to isometries. We also investigate radial solutions to the related $p$-Laplace Lane-Emden equation, obtaining rigidity of finite-energy solutions regardless of optimality. Furthermore, we study the asymptotic behavior of infinite-energy solutions.
  • Classification : 35B53, 35J92, 58J05, 58J70, 46E35
  • Author(s) :
    • Matteo Muratori (Politecnico di Milano)
    • Nicola Soave (Politecnico di Milano)