Linear and Quasi-linear Equations of Parabolic Type

addition analogous arbitrary assertions assume assumptions belongs boundary value problems bounded carried Cauchy problem Chapter Chapter II classical coefficients connection consequently consider constant continuous converge cylinder defined definition depending derivatives determined differential distance domain dx dt easily elements equal to zero equation equation 1.1 established estimate example existence fact finite formulate function u(x given gives hence Hölder holds identity indicated inequality initial integral known Lemma limit linear means method namely necessary norm obtain operator parabolic positive possible present proof properties proved quantities relation respect restrictions result right side satisfy smooth solution solvability space sufficiently Suppose surface t₁ Theorem tion transform unique valid virtue vrai max ди