alpha int b u frac partial u partial x mathrm dx math using math display block int b u frac partial u partial mathrm dx frac frac partial partial u quad text quad int b u frac partial u partial x mathrm dx frac u bt frac u math integration parts used second relationship get math display block frac partial partial u alpha u bt alpha u math math cdot math denotes standard l norm well posedness require energy solution non increasing ie
Formal science Mathematics Pure mathematics Analysis Partial differential equations