Singular Solutions to a (3 + 1)-D Protter-Morawetz Problem for Keldysh-Type Equations

<div>(a) Guderley-Morawetz domain. (b) Protter-Morawetz domain <span class="nowrap"><svg height="11.974pt" id="M113" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.9242 9.97754 11.974" width="9.97754pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.646,-2.897)"><path d="M658 624L641 649C599 612 554 595 493 595C444 595 402 603 342 615C268 634 232 641 184 641C129 641 57 621 0 557L17 532C67 566 113 586 176 586C230 586 265 577 316 565C380 550 430 540 482 540C540 540 611 558 658 624Z" id="g119-113"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path></g></svg>.</span></div>

Advances in Mathematical Physics

fig2

Figure 2

Figure 2: Singular Solutions to a (3 + 1)-D Protter-Morawetz Problem for Keldysh-Type Equations 