We consider the one-dimensional one phase Stefan problems with temperature or thermal flux boundary conditions. Exact and closed-form solutions for these two free boundary problems are very limited ...

As pinch-off is approached, the length and timescales near the singularity become much smaller than the scale of the initial conditions that caused the singularity to form. In this regime the ...

Coagulation–fragmentation equations model the time evolution of systems in which particles or clusters dynamically merge or break apart. These equations play a crucial role in diverse fields ranging ...

The dissipative two dimensional Quasi-Geostrophic Equation (2D QGE) is studied. First, we prove existence and uniqueness of the solution, local in time, in the critical Sobolev space H2–2α with ...