18 citations · 21 across the 9 of their papers we have counts for
4 papers · 1 filter
Energy balance and damage for dynamic brittle fracture from a nonlocal formulation
Robert P. Lipton, Debdeep Bhattacharya
A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inela…
Quasistatic Evolution with Unstable Forces
Debdeep Bhattacharya, Robert P. Lipton
We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniq…
Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov-Kuznetsov equation
Debdeep Bhattacharya
We consider the focusing modified Zakharov-Kuznetsov (mZK) equation in two space dimensions. We prove that solutions which blow up in finite time in the norm have the…
Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation
Debdeep Bhattacharya, Luiz Gustavo Farah, Svetlana Roudenko
We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the -method, we prove the global well-posedness o…